Question

In right triangle abc, angle a and angle b are complementary angles. the value of cos a is 5/13. what is the value of sin

Answer 1

cos is $\frac{adjacent}{hypotenuse}$. So, if cos(a)= $\frac{5}{13}$ then use Pythagorean Theorem to determine the length of the "opposite" side.

5² + x² = 13²

25 + x² = 169

      x² = 144

       x = 12

Now that you know the length of the opposite side, you can plug it in for sin.

sin is $\frac{opposite}{hypotenuse}$. So, sin(a) = $\frac{12}{13}$

Now, if you switch so you are looking for sin(b), the cos and sin also switch.

cos(b) = sin(a) = $\frac{12}{13}$

sin(b) = cos(a) = $\frac{5}{13}$

Answer: sin(b) = $\frac{5}{13}$

Answer 2

He’s right ^^**^^^^^^^^