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48. Amari is observing a woodpecker near the top of a tree,
as shown in the diagram below. What is the measure of
angle x, the angle of elevation, rounded to the nearest
degree?
bird
201
36 n

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Here x is the angle of the elevation and the value of x is 31 degrees.

We have given that,

Amari is observing a woodpecker near the top of a tree,

as shown in the diagram given.

We have to determine,

The measure of angle x, the angle of elevation, is rounded to the nearest degree.

What is the formula for tan theta?

$$tan(\theta)=\frac{Opposite \ side}{Hypotenuse}$$

From the diagram,

Opposite side=20ft

Use this value of the above formula.

So we get,

$$tan(\theta)=\frac{20}{36} \\\\tan(x)=5/9\\\\tan(x)=0.55\\x=tan^{-1}(0.55)\\x=31.51^0$$

Here x is the angle of the elevation and the value of x is 31 degrees.

Therefore the value of x is 31.