28.8k views
4 votes
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.

User Mark Lavin
by
7.9k points

1 Answer

3 votes

Answer:

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

User Giu
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories