Question

Which one of the following is an obtuse triangle?
A)

B)

C)

Answer 1

Hint:
An obtuse triangle has one angle greater than ${90^ \circ }$ and less than ${180^ \circ }$. A right-angled triangle has one angle equal to ${90^ \circ }$. An acute triangle has all the angles measuring less than ${90^ \circ }$.

Complete step by step solution:
An obtuse angle is an angle which is greater than ${90^ \circ }$ and less than${180^ \circ }$. The triangle has an obtuse angle is known as the obtuse triangle. An obtuse triangle has only one obtuse angle because the sum of all angles of a triangle is equal to ${180^ \circ }$. The side opposite to the obtuse angle is the longest side o the triangle.
In the first figure A,

We can see that two angles are less than ${90^ \circ }$ which means they are acute angles and one angle is greater than ${90^ \circ }$ but less than ${180^ \circ }$ so it is an obtuse angle. Hence this triangle is an obtuse triangle.
In figure B,

We can see that one angle is equal to ${90^ \circ }$ and other angles are acute angles. Hence it is a right-angled triangle.
In figure C,

We see that all angles are less than ${90^ \circ }$ which means they are all acute angles. Hence the triangle is an acute triangle.

Hence the correct answer is A.

Note:
There are some important formulae related to the obtuse triangle-
1) If we have to calculate the length of the sides of the triangle we use the formula- ${a^2} + {b^2} < {c^2}$ where c is the longest side and the lengths of the triangle are a, b, c.
2) Area of the triangle is=$\dfrac{1}{2} \times \left( {b \times h} \right)$ where b is base and h is height of triangle.
3) The perimeter of the triangle is equal to the sum of the sides of the triangle. Perimeter=$a + b + c$ where a, b, c are the length of the sides of the triangle.