Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/2`, the angle between sides B and C is `pi/3`, and the length of B is 8, what is the area of the triangle?

Answer 1

The area of the triangle is `55.43(2dp)` sq.unit

Explanation:

The angle between sides `A and B` is `/_c=pi/2=180/2=90^0`

The angle between sides `B and C` is `/_a=pi/3=180/3=60^0`

This is a right triangle with base `B=8 :. tan a = A/B or A= B *tana :. A = 8 *tan60 =8*sqrt3`

The area of the triangle is `A_t= 1/2 * B* A= 1/2*8*8*sqrt3 = 32* sqrt3=55.43(2dp)` sq.unit [Ans]