The equation relating the acute angles A and C is (a) tan(A) = sin(A)/sin(C)
How to determine the equation relating the acute angles
From the question, we have the following parameters that can be used in our computation:
The right triangle ABC
Also, we have the trigonometry identity
tan(X) = sin(X)/cos(X)
In a right triangle with acute angles A and C, we have
sin(A) = cos(C) and sin(C) = cos(A)
Using the above as a guide, we have the following:
tan(A) = sin(A)/cos(A) and
tan(C) = sin(C)/cos(C)
Recall that
sin(A) = cos(C) and sin(C) = cos(A)
So, we have
tan(A) = sin(A)/sin(C)
Hence, the equation relating the acute angles is (a) tan(A) = sin(A)/sin(C)