Question

Which trigonometric ratios are correct for triangle XYZ?

Check all that apply.
tan(Y) = 15
cos(x) = 17
tan(x) =
sin(y) =
COS(Y) = 1;

Answer 1

a c d

Explanation:

trust

Answer 2

`tan(Y)=(8)/(15)`

`tan(X)=(15)/(8)`

`sin(Y)=(8)/(17)`

Explanation:

The complete question in the attached figure

Verify each case

Part 1) tan(Y)

we know that

The tangent of angle Y is equal to divide the opposite side angle Y by the adjacent side to angle Y

so

`tan(Y)=(XZ)/(YZ)`

substitute the given values

`tan(Y)=(8)/(15)`

Part 2) cos(X)

we know that

The cosine of angle X is equal to divide the adjacent side angle X by the hypotenuse

so

`cos(X)=(XZ)/(XY)`

substitute the given values

`cos(X)=(8)/(17)`

Part 3) tan(X)

we know that

The tangent of angle X is equal to divide the opposite side angle X by the adjacent side to angle X

so

`tan(X)=(YZ)/(XZ)`

substitute the given values

`tan(X)=(15)/(8)`

Part 4) sin(Y)

we know that

The sine of angle Y is equal to divide the opposite side angle Y by the hypotenuse

so

`sin(Y)=(XZ)/(XY)`

substitute the given values

`sin(Y)=(8)/(17)`

Part 5) cos(Y)

we know that

The cosine of angle Y is equal to divide the adjacent side angle Y by the hypotenuse

so

`cos(Y)=(YZ)/(XY)`

substitute the given values

`cos(Y)=(15)/(17)`