Obtuse Triangle

FAQs on Obtuse Triangle

1. What is an obtuse triangle?

   An obtuse triangle is a type of triangle where one of its angles is greater than 90° but less than 180°. The other two angles in obtuse triangle will always be acute (less than 90°).

2. How do you identify an obtuse triangle?

   You can identify an obtuse triangle by checking its angles. If any one of the three angles measures more than 90°, then it is an obtuse triangle.

3. What is the sum of the angles in an obtuse triangle?

   The sum of all three interior angles in an obtuse triangle is always 180°, just like any other triangle.

4. Can a triangle have more than one obtuse angle?

   No, a triangle cannot have more than one obtuse angle. Since the sum of all angles in any triangle is 180°, having two obtuse angles (each greater than 90°) would exceed this sum, which is not possible in triangle.

5. What are the properties of an obtuse triangle?

   • One of the angles is greater than 90°.
   • The sum of all three angles is 180°.
   • The side opposite the obtuse angle is always the longest side.
   • It can be either a scalene or an isosceles triangle but never an equilateral triangle.

6. Can an obtuse triangle be a right triangle?

   No, an obtuse triangle cannot be a right triangle because a right triangle has one angle measuring exactly 90°, while an obtuse triangle must have one angle greater than 90°.

7. Can an obtuse triangle be isosceles?

   Yes, an obtuse triangle can be isosceles if it has two equal sides and one obtuse angle. However, it cannot be equilateral, as all angles in an equilateral triangle are 60°.

8. How do you calculate the area of an obtuse triangle?

   The area of an obtuse triangle can be found using the formula below if base and height of the triangle is known.

   $$\text{Area}=\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$$
   Alternatively, if you know the three sides of obtuse triangle you can use Heron’s formula.
   $A=\sqrt{(s-a)(s-b)(s-c)}$

   where

   • $s$ is the semi-perimeter of the triangle, $(s=\frac{a+b+c}{2})$
   • $a$, $b$, and $c$ are the three sides of the triangle.

9. What are some real-life examples of obtuse triangles?

   Obtuse triangles can be found in various real-world structures and objects, such as:

   • Roof trusses in architecture
   • Certain types of road signs
   • Kite shapes
   • Mountain peaks and landscapes

10. Why can a triangle have only one obtuse angle?

    A triangle’s total angle sum is always 180°. If a triangle had two obtuse angles (each greater than 90°), their sum would exceed 180°, which is impossible in triangle.

11. How do you find the height of an obtuse triangle?

    To find the height, drop a perpendicular line from the obtuse angle’s vertex to the opposite side (or its extension). This height is outside the triangle rather than inside, unlike in acute triangles.