Question

In ΔABC, ∠B is a right angle, AB = 30, and sec A = 5/3. Find the value of csc C in fraction and in decimal form.

Answer 1

sec(A) = 5/3   ⇒   cos(A) = 3/5

Angles A and C are complimentary (they sum to 90°), so

sin(C) = cos(A) = 3/5

since sin(90° - x) = cos(x) for all x, and in turn

csc(C) = 1/sin(C) = 5/3