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

b.

Answer 1

He’s right ^^**^^^^^^^^

Answer 2

cos is
`(adjacent)/(hypotenuse)`. So, if cos(a)=
`(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
`(opposite)/(hypotenuse)`. So, sin(a) =
`(12)/(13)`

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

cos(b) = sin(a) =
`(12)/(13)`

sin(b) = cos(a) =
`(5)/(13)`

Answer: sin(b) =
`(5)/(13)`