Question

For the right triangle shown match the equivalent expressions.

Answer 1

The one above me is correct

Explanation:

I just wanted people to get the right answer

Answer 2

Part a)
`cos(A)=sin(B)`

Part b)
`cos(B)=sin(A)`

Part c)
`sin(A)=cos(B)`

Part d)
`sin(B)=cos(A)`

Explanation:

we know that

In the right triangle ABC of the figure

`A+B=90\°` ----> by complementary angles

so

`cos(A)=sin(B)`

`sin(A)=cos(B)`

Part a) Cos(A)

`cos(A)=sin(B)`

`cos(A)=(5)/(13)`

The value of cosine of angle A is the ratio between the adjacent side angle A to the hypotenuse

Part b) Cos(B)

`cos(B)=sin(A)`

`cos(B)=(12)/(13)`

The value of cosine of angle B is the ratio between the adjacent side angle B to the hypotenuse

Part c) Sin(A)

`sin(A)=cos(B)`

`sin(A)=(12)/(13)`

The value of sine of angle A is the ratio between the opposite side angle A to the hypotenuse

Part d) Sin(B)

`sin(B)=cos(A)`

`sin(B)=(5)/(13)`

The value of sine of angle B is the ratio between the opposite side angle B to the hypotenuse