Question

In this figure, sin(a) = 23

What is the value of cos(b) ?A)13
B)23
C)23
D)32 please help and show work if possible

Answer 1

$a$ and $b$ are complementary, or $b=\dfrac\pi2-a$. So

$\cos b=\cos\left(\dfrac\pi2-a\right)=\sin a$

and so $\cos b=\dfrac23$.