Question

In right triangle ABC with the right angle at C. sin A = 2x + 5 and cos B =

4x - 17. Determine and state the value of x.

Answer 1

11

Explanation:

Given triangle ABC is right angled at C.

Therefore

A + B + 90 = 180

A + B = 180 - 90 = 90

B = 90 -A

Given

sin A = 2x + 5 ----------------------->A

cos B = 4x - 17 ----------------------->B

Also B = 90 - A

Substituting value of B in terms of A in equation B

we have

Cos 90 - A = 4x - 17 ( we know that cos(90-A) = sin A)

=>Sin A = 4x - 17 ----------------------->C

also it is given that sin A = 2x + 5

equating equation A and C we have

2x + 5 = 4x - 17

=> 4x - 2x = 5 + 17

=> 2x = 22

=> x = 22/2 = 11

X is 11