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____ [38]
3 years ago
13

looks out from the crown of the Statue of Liberty, approximately 250 ft above ground. The tourist sees a ship coming into the ha

rbor and measures the angle of depression as 18°. Find the distance from the base of the statue to the ship to the nearest foot.

Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

The distance from the base of the statue to the ship is 771.60 ft

Step-by-step explanation:

Refer the attached figure

Height of statue AB= 250 feet

The tourist sees a ship coming into the harbor and measures the angle of depression as 18°.

So, ∠ACB = 18°

We are supposed to find the distance from the base of the statue to the ship i.e. BC

In ΔABC

Tan \theta = \frac{Perpendicular}{Base}

Tan 18^{\circ}=\frac{AB}{BC}

Tan 18^{\circ}=\frac{250}{BC}

BC=\frac{250}{Tan 18^{\circ}}

BC=\frac{250}{0.324}

BC=771.60 ft

Hence the distance from the base of the statue to the ship is 771.60 ft

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