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

Answer:

sin(X)=cos(Z)

Step-by-step 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

 $\implies sin(X)=\dfrac{27}{45}\\\\\implies sin(X)=\dfrac35$

trig ratio cos(x) = A/H

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

So if A = 27 and H = 45 then

$cos(Z)=\dfrac{27}{45}\\\\\implies cos(Z)=\dfrac{3}{5}$

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