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Which is the best approximation for the measure of angle XYZ

Which is the best approximation for the measure of angle XYZ-example-1
User LexLythius
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2 Answers

1 vote
The correct answer is


39.8


but please correct me if im wrong
User SuperMind
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8.3k points
6 votes

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)

User Dan Chase
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