Question

In the right triangle below, sin X= 3/5. This is the same as the cosine of which angle? Explain why this is true.

Answer 1

sin(X)=cos(Z)

Explanation:

trig ratio sin(x) = O/H

(where O = side opposite the angle and H = hypotenuse)

Therefore, if angle = X, O = 27 and H = 45

`\implies sin(X)=(27)/(45)\\\\\implies sin(X)=\frac35`

trig ratio cos(x) = A/H

(where A = side adjacent to the angle and H = hypotenuse)

So if A = 27 and H = 45 then

`cos(Z)=(27)/(45)\\\\\implies cos(Z)=(3)/(5)`

Therefore,
`sin(X)=cos(Z)`