Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s)
a right triangle abc has complementary angles a and c.
if sin(a) = \frac{24}{25}, the value of cos(c) =
if cos(c) = \frac{20}{29}, the value of sin(a) =

Explanation:

Step1: Relate angles A and C

Since angles A and C are complementary, \(A + C = 90^\circ\), so \(C = 90^\circ - A\).

Step2: Use cosine of complementary angle

\(\cos(C) = \cos(90^\circ - A) = \sin(A)\).

Step3: Substitute sin(A) value

Given \(\sin(A) = \frac{24}{25}\), so \(\cos(C) = \frac{24}{25}\).

Step4: Reverse the relationship

For the second part, \(\sin(A) = \sin(90^\circ - C) = \cos(C)\).

Step5: Substitute cos(C) value

Given \(\cos(C) = \frac{20}{29}\), so \(\sin(A) = \frac{20}{29}\).

Answer:

24/25
20/29