From Wikipedia, the free encyclopedia An acute triangle (or acute-angled triangle ) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle ) is a triangle with one obtuse angle (greater than 90°) and two acute angles.
- 1 Do all triangles have 3 acute angles?
- 2 Do all triangles have 3 acute angles True or false?
- 3 How many acute angles are in an obtuse triangle?
- 4 Can a triangle have 3 acute sides?
- 5 Can a triangle have all acute angles?
- 6 Can a triangle have 2 obtuse angles?
- 7 Can 1 acute and 2 obtuse form a triangle?
- 8 Is a 45-45-90 triangle acute?
- 9 Is 47 degrees an acute angle?
- 10 Can 3 angles be acute?
How many angles are acute?
Fun Facts – 1. At least two angles of any triangle are acute angles.2. In a 180˚angle, if one angle is obtuse (more than 90˚), the other will always be an acute angle (less than 90˚).
Do all triangles have 3 acute angles?
A triangle can have all three angles acute. It can have one angle 90 degrees and the other two acute. It can have one obtuse angle and the two other angles will be acute.
Do all triangles have 3 acute angles True or false?
Yes, all triangles have at least two acute angles. Acute angles are angles that measure less than 90 degrees, while obtuse angles measure greater than 90 degrees.
How many acute angles are in an obtuse triangle?
An triangle has one obtuse angle and two acute angles. No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Open in App Suggest Corrections 3 : An triangle has one obtuse angle and two acute angles.
Do acute angles equal 180?
Angles between 0 and 90 degrees (0° Angles between 90 and 180 degrees (90°. Angles that are 90 degrees (θ = 90°) are right angles. Angles that are 180 degrees (θ = 180°) are known as straight angles.
Are all acute angles 45 degree?
Acute Angle Degree – The degree of an acute angle measures less than 90 degrees, i.e. less than a right angle. The examples of acute angle degrees are 12°, 35°, 48°, 65°, 80°, 89°. Hence, the acute angle degree ranges from 0 degrees and less than 90 degrees.
Can a triangle have 2 acute angles?
A triangle can have two acute angles. Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! Open in App Suggest Corrections 14 : A triangle can have two acute angles.
Can a triangle have 3 acute sides?
Practice Questions –
- If two angles of an acute-angled triangle are 85 o and 30 o, what is the angular measurement of the third angle?
- Find the area of the triangle if the length of one side is 8 cm and the corresponding altitude is 6 cm.
- Construct an acute angle triangle which has a base of 7 cm and base angles 65 o and 75 o, Find the circumcenter and orthocenter.
Yes, all equilateral triangles are acute angle triangles. It is because an equilateral triangle has three equal angles, i.e.60° each which are acute angles. To find the third angle of an acute triangle, add the other two sides and then subtract the sum from 180°.
Thus, the formula to find the third angle is ∠A + ∠B + ∠C = 180°. Yes, an acute scalene triangle is possible if the interior angles of the scalene triangles are acute. Not only scalene, but an acute triangle can also be an isosceles triangle if it satisfies its condition. A triangle can never have only one acute angle.
If a triangle has 1 acute angle, the other angles will be either right angles or obtuse angles which is not possible as the sum of interior angles of a triangle is always 180°. So, every triangle needs to have at least 2 acute angles. Triangles can be categorized into two main types, i.e.
based on their sides or based on their interior angles. These two categories can also be further classified into various types like equilateral, scalene, acute, etc. To learn all the different types of triangles with detailed explanations, click here- To learn more about other types of triangles and related topics in Geometry, register with BYJU’S – The Learning App.
: Acute Angle Triangle- Definition, Properties, Formulas, Questions
Do all triangles have exactly 2 acute angles?
Answer and Explanation: There are two types of triangles that have exactly two acute angles: right triangles and obtuse triangles. Right triangles contain one right angle, which measures exactly 90 degrees, and two acute angles, which measure less than 90 degrees.
Can a triangle have all acute angles?
Flexi Says: When classifying a triangle by its angles, you should look at the size of the angles:
- A triangle with one right angle and two acute angles is a right-angled triangle,
- A triangle with all three acute angles is an acute triangle,
- A triangle has one obtuse angle and two acute angles is an obtuse triangle,
Click here to learn more about triangles! – Want to learn more? Go to Lesson Page
Can a triangle have 2 obtuse angles?
Obtuse Triangle – Definition, Properties, Formulas, Examples An obtuse-angled triangle is a triangle in which one of the measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°. For better understanding, look at the following example. In this image, triangle XYZ has an obtuse angle at Y, Therefore, this triangle is an obtuse-angled triangle. Note that the other two angles are less than 90 degrees, and all the angles of the triangle add up to 180 degrees. A cloth-hanger has an obtuse angle where the hook is attached at the top. In the above examples, we can clearly see that the triangle shapes do not have an angle greater than 90°. Therefore, this is not an obtuse triangle.
- An can never be obtuse. Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled.
- A cannot be right-angled and obtuse-angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute. Therefore, an obtuse-angled triangle can never have a right angle and vice versa.
- The side opposite the obtuse angle in the triangle is the longest.
Isosceles obtuse triangle: Here, two sides of the triangle have equal lengths.
Scalene obtuse triangle: All sides are unequal in this type of obtuse triangle.
Is the following picture an example of an obtuse triangle?
Answer: No, the given figure is not an obtuse triangle as all the angles are less than 90°.
Will the following set of angles form an obtuse triangle?
95°, 30°, 55°. Answer: Yes, these angles will form an obtuse-angled triangle, as 95 degrees is an obtuse angle and the sum of the angles(95 + 30 + 55) is 180 degrees.
What type of obtuse triangle is shown in the figure?
Answer: It is an obtuse scalene triangle as none of its sides are equal. Attend this Quiz & Test your knowledge. Correct answer is: 105°, 65°, 10°An obtuse triangle has one obtuse angle. The other two angles are acute angles. Correct answer is: 35° eachThe sum of the other two angles is 180° − 110° = 70°.
Hence, the other two angles will measure 35° each. Correct answer is: 13 cmsPerimeter of the obtuse triangle = 3 + 4 + 6 = 12 cm Can a triangle have two obtuse angles? No, a triangle cannot have two obtuse angles, as the sum of the three angles cannot exceed 180 degrees. How do you distinguish between acute and obtuse triangles? Obtuse triangles have one angle that’s greater than 90°.
In, all the angles are less than 90°. Can an obtuse triangle have one right angle? No, a triangle cannot have both obtuse and, as the sum of the three angles cannot exceed 180 degrees. How do you know if a triangle is obtuse? We can easily identify an obtuse triangle by looking at its angles.
Can 2 acute and 1 right form a triangle?
Triangles can be classified in the following manner:
acute triangle- a triangle with 3 acute angles right triangle- a triangle with one right angle obtuse triangle- a triangle with one obtuse angle equiangular triangle- a triangle with 3 congruent 60 degree angles
scalene triangle- a triangle with no congruent sides isosceles triangle- a triangle with at least 2 congruent sides equilateral triangle- a triangle with 3 congruent sides
All equilateral triangles are equiangular. All equiangular triangles are equilateral. A right triangle will have 1 right angle and 2 acute angles. An obtuse triangle will have 1 obtuse triangle and 2 acute angles.
Return to the Triangle Classification Menu
Can 1 acute and 2 obtuse form a triangle?
No, a triangle cannot have 2 obtuse angles. The definition of an obtuse angle is an angle with a measure that is greater than 90°. Therefore, if the measures of the angles of a triangle were a, b, and c, where a and b are obtuse angles and c > 0°, then we would have the following: a + b + c > 90° + 90° + c = 180° + c.
How many acute angles can a right triangle have?
How many acute angles can a right triangle have? Join Vedantu’s FREE Mastercalss Answer Verified Hint: Here we have to determine the number of possible acute angles in a right-angled triangle. We know that a triangle is defined as a regular polygon, which has three sides and the sum of any two sides of the triangle is always greater than the third side.
- We will use the definition of the right angle triangle here and also the important properties of the triangle to get the required answer.
- Complete step by step solution: Here we have to determine the number of possible acute angles in a right-angle triangle.A right-angled triangle is one of the types of triangles that has 3 sides’ i.e.
the base, hypotenuse, and the perpendicular in which the angle between the base and height is equal to $90 ^\circ $. We will draw the triangle $ABC$ which is right-angled at $B$. We also know that the sum of all the angles of the triangle is equal to $180 ^\circ $.We will sue this property here in this triangle.$ \angle A + \angle B + \angle C = 180^\circ $We know that the value of $\angle B = 90^\circ $. So we will substitute the value here.$ \Rightarrow \angle A + 90^\circ + \angle C = 180^\circ $Now, we will subtract $90^\circ $ from both sides.$ \Rightarrow \angle A + 90^\circ + \angle C – 90^\circ = 180^\circ – 90^\circ \\ \Rightarrow \angle A + \angle C = 90^\circ \\ $Thus, both of the remaining two angles must have a measure less than $90^\circ $ and therefore must be acute.
Hence, the right triangle can have only two acute angles. Note:
Here we have obtained the number of possible acute angles in a right-angled triangle. We know that acute angles are the angles that are less than $90^\circ $, whereas the obtuse angle is an angle that is greater than $90^\circ $. We also know that a straight line makes $180^\circ $ whereas the reflex angle is an angle that is greater than $1800^\circ $ but less than $360^\circ $.
What is a 72 degree angle called?
Now, we can see that 72 degrees is an acute angle so it will be less than 90 degrees.
What is a 75 degree angle called?
An angle whose measure is more than 0° but less than 90° is called an acute angle.75° is less than 90°. So it is acute angle.
What is a 150 degree angle called?
Obtuse angle -an angle between 90 and 180 degrees.
Is a 45-45-90 triangle acute?
45-45-90 triangles are right triangles whose acute angles are both 4 5 ∘ 45^\circ 45∘. This makes them isosceles triangles, and their sides have special proportions: A forty-five-forty-five-ninety triangle. The length of both legs are k units.
What is a 200 degree angle called?
– Reflex Angle Reflex angles are the types of angles whose degree measurement is more than 180° but less than 360°. Common examples of reflex angles are; 200°, 220°, 250°, 300°, 350°, etc.
Is 47 degrees an acute angle?
Acute Angle – Acute Angle An acute angle lies between 0 degree and 90 degrees, or in other words; an acute angle is one that is less than 90 degrees. The figure above illustrates an acute angle.
Are all 30 degree angles acute?
A 30-degree angle is an acute angle. An angle is formed when two lines meet or intersect at a point. An acute angle is one in which the measure of the angle is less than 90 degrees.
Can 3 angles be acute?
What is Acute Triangle? – Definition Facts & Example A triangle is a basic polygon with three sides and three vertices. Since it has three sides, it has three interior angles. An angle that measures between 0° and 90° is called an acute angle. An acute is a type of triangle in which all the three of the triangle are acute. We can categorize acute triangles into three different types based on the side length and angles of the triangles as follows. Equilateral Triangle All the sides of an are of equal lengths—each interior angle of this triangle measures 60°. So, an equilateral triangle is always an acute triangle.
- In the given figure of an equilateral Triangle,
- ∠A = ∠B = ∠C = 60°
- Side AB = Side BC = Side AC
- Acute Isosceles Triangle
- Two sides of an acute isosceles triangle are of equal length, and angles opposite to those sides measure the same.
- In the given figure of an Acute Isosceles Triangle,
- ∠B = ∠C ≠ ∠ASide AB = Side AC ≠ Side BC
All three sides and internal angles of a scalene acute triangle are unequal. All angles measure less than 90 degrees. In the given figure of an Acute Scalene Triangle, ∠A ≠ ∠B ≠ ∠C Side AB ≠ Side BC ≠ Side AC The basic formulas relating to an acute triangle is to calculate its perimeter and area. Perimeter measures the outer boundary of the given shape. The perimeter of a triangle is the sum of the length of all the sides. The area of a triangle means the inner space covered by the three sides of the triangle. The of an acute triangle can be calculated using the formula of the area of a triangle. Area of triangle = (1/2) × b × h Here, ‘b’ is the base length of an acute triangle, and ‘h’ is the height of an acute triangle.
- Using the angle sum property of triangles, we get ∠A = 180° – 70° – 30° = 80°.
- Since all three angles of the given triangle are different acute angles, it is an acute scalene triangle.
In an acute isosceles triangle ABC, side AB = 6 cm and ∠B = ∠C. If the perimeter of this triangle is 16 cm, then find the length of the side BC.
Solution: In the given acute isosceles triangle ABC, ∠B = ∠C. The sides opposite these angles are equal. Therefore, the lengths of the sides AB and AC must be equal. So, AB = AC = 6 cm The perimeter of the triangle is 16 cm. Therefore, AB + AC + BC = 16 cm. So, the length of the side BC must be 16 – 6 – 6 or 4 cm.
Find the area of the acute triangle whose base is 5 cm long and height is 6 cm?
- Area of an acute triangle = Area of a triangle = (1/2) × b × h.
- Substituting the value of the base (b) as 5 cm long and height (h) as 6 cm, we get
- Area = 1/2 × 5 × 6 = 15 cm 2
Attend this Quiz & Test your knowledge. Correct answer is: 60°, 70°, 50°In an acute triangle, all the three angles are less than 90°. Only option a) satisfies this condition. Correct answer is: Acute Isosceles Triangle All the three interior angles ∆ABC are acute and AB = AC.
Therefore, ∆ABC is an acute isosceles triangle. Correct answer is: Acute Scalene TriangleUsing the angle sum property of a triangle, we get $x + x + 20 + x + 40 = 180$. So, x must be 40 and the three interior angles of the triangle are 40°, 60° and 80°. Since all the angles of the triangle are acute but different, the triangle must be an Acute Scalene Triangle.
An angle that measures between 0° and 90° is called an acute angle. It can be measured using a protractor. What are the properties of an acute angled triangle? The significant properties of an acute triangle are:
- All the three interior angles of an acute triangle measures less than 90°.
- The angles of an acute triangle add up to 180°.
Is a scalene triangle always an acute triangle? No, a scalene may not always be an acute triangle. It can be a right-angled triangle with the angles of 90°, 40°, and 50°. A can also be an with angles as 30°, 50°, and 100°. Three interior angles of an acute triangle must be less than 90°.