Question

ZAP is a right triangle, with right angle A and cosP = 4/5. What is sin Z?

Answer 1

if you want to find cosP , since angles Z and P are 2 complementary angles then cosZ is the same as cosP so you say the cosP=sinZ=4/5 (property of 2 complement angles in a right triangle)

Answer 2

`\text{sin}(Z)=(4)/(5)`.

Explanation:

We have been given that ZAP is a right triangle, with right angle A and
`\text{cos}(P)=(4)/(5)`. We are asked to find the
`\text{sin}(Z)`.

Please find the attachment.

We know that
`\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}` and
`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`.

Upon looking at our attachment, we can see that
`\text{cos}(P)=\text{sin}(Z)`, therefore,
`\text{sin}(Z)=(4)/(5)`.