Chapter 12.6, Problem 5CE

To determine

To determine the length of third angle and the two sides.

Explanation of Solution

Given information :

Length of two sides is given.

Two acute angles are given.

Let us assume the given angles and sides.

Let us assume sides of the triangle be a, b, and c. And angles A, B, and C.

Thus the triangle so formed is,

  

Whenever two sides and two angles are given and we have to find third side, we shall use cosine law. Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Third angle can be determined directly as we know that the sum of all angles of triangle is ${180}^{\circ }$ . Hence we can subtract the given two from ${180}^{\circ }$ . And sides can be determined using cosine law.