Question

Which of the following trig expressions could be used to find m<7?

Answer 1

Part 1)
`m\angle Z=tan^(-1)((14)/(6))`

Part 2)
`m\angle Y=tan^(-1)((6)/(14))`

Explanation:

Part 1) Find the measure of angle Z

we know that

In the right triangle XYZ of the figure

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

so

`tan(Z)=(XY)/(XZ)`

substitute the given values

`tan(Z)=(14)/(6)`

`m\angle Z=tan^(-1)((14)/(6))`

Part 2) Find the measure of angle Y

we know that

In the right triangle XYZ of the figure

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

so

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

substitute the given values

`tan(Y)=(6)/(14)`

`m\angle Y=tan^(-1)((6)/(14))`