Question

Angles C and D are acute angles of a right triangle.

Answer 1

Answer:

The answer to your question is cos C =$\frac{5}{7}$

Step-by-step explanation:

Data

sin D = $\frac{5}{7}$

Formula

sine Ф = $\frac{opposite side}{hypotenuse}$

- If sin D = $\frac{5}{7}$

the opposite side = 5

the hypotenuse = 7

- We can find the adjacent side of angle D using the pytagorean theorem

               7² = a² + 5²

               a² =49 - 25

               a² = 24

               a = $\sqrt{24}$

- To find the cosine of angle C

 Cos C = $\frac{adjacent side}{hypotenuse}$

  Cos C = $\frac{5}{7}$

                  sin D = cos C