Question

Which is the best approximation for the measure of angle XYZ

Answer 1

The correct answer is


39.8


but please correct me if im wrong

Answer 2

Answer:
`39.8^(\circ)`

Explanation:

In the given picture , we have a right triangle.

Let x represents ∠XYZ.

The side opposite to angle x = 10 in.

The side adjacent to angle x = 12 in.

By trigonometry, we have

`\tan x=\frac{\text{Side opposite to x}}{\text{Side adjacent to x}}`

`\Rightarrow\tan x=(10)/(12)=0.833333333\\\\\Righatrrow\ x=\tan ^(-1)(0.83333333)=0.69473826`

In degrees,
`x=0.69473826*(180^(\circ))/(\pi)\approx39.8^(\circ)`

Hence, the best approximation for the measure of ∠XYZ is
`39.8^(\circ)`