Answer:
11
Step-by-step 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
