etch and Solve each problem given below. Round your answers to two decimal places.
1.) The angle of elevation from point to the top of a hill is . If point is 400 feet from the
base of the hill, how high is the hill?
2.) Find the angle of elevation of the sun when a 12.5 -meter-tall telephone pole casts a 18 -meter-
long shadow.

Ask by Reed Marshall. in the Philippines

Mar 20,2025

Question

etch and Solve each problem given below. Round your answers to two decimal places.
1.) The angle of elevation from point to the top of a hill is . If point is 400 feet from the
base of the hill, how high is the hill?
2.) Find the angle of elevation of the sun when a 12.5 -meter-tall telephone pole casts a 18 -meter-
long shadow.

Ask by Reed Marshall. in the Philippines

Mar 20,2025

UpStudy AI · Accepted Answer

1.) We are given the angle of elevation $$ \theta = 49^{\circ} $$ and the horizontal distance $$ d = 400 $$ feet. For a right triangle, the tangent of the angle is the ratio of the opposite side (hill height $$ h $$) to the adjacent side (distance $$ d $$). Thus, we have

$$
\tan(49^{\circ}) = \frac{h}{400}.
$$

Solving for $$ h $$:

$$
h = 400 \cdot \tan(49^{\circ}).
$$

Using a calculator for $$ \tan(49^{\circ}) $$:

$$
\tan(49^{\circ}) \approx 1.15.
$$

Thus,

$$
h \approx 400 \cdot 1.15 \approx 460.16 \text{ feet}.
$$

2.) We are given the telephone pole height $$ H = 12.5 $$ meters and the length of the shadow $$ s = 18 $$ meters. The angle of elevation $$ \theta $$ is given by the relationship:

$$
\tan(\theta) = \frac{H}{s} = \frac{12.5}{18}.
$$

Calculating the quotient:

$$
\frac{12.5}{18} \approx 0.69.
$$

To find the angle $$ \theta $$, take the inverse tangent:

$$
\theta = \arctan(0.69).
$$

Using a calculator:

$$
\theta \approx 34.99^{\circ}.
$$

Thus, the angle of elevation of the sun is approximately $$ 34.99^{\circ} $$.
1.) The hill is approximately 460.16 feet high. 2.) The angle of elevation of the sun is approximately 34.99 degrees.

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