A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8o when staring at the top of the stat

Question

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A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8o when staring at the top of the stat

ue. Then the person looks down at an angle of 14o when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-03-05T06:38:39+03:00

Answer:

$h=50.25\ ft$

Step-by-step explanation:

Right Triangles

In a right triangle, one angle measures 90°. This forms a hypotenuse, which is the longest side, alongside two short sides known as legs. These elements are connected to Pythagoras's theorem, and the fundamental trigonometric relationships also apply, including

$\displaystyle tan\alpha=\frac{a}{c}$

where a represents the leg opposite $\alpha$ and c denotes the adjacent leg.

In this scenario, a statue is observed by a person positioned 50 ft away. The observer looks upwards at an elevation angle of 8° towards the statue's top and then downwards at a 14° angle toward the statue's base. The illustration below depicts the situation.

The statue's height is expressed as h=a+b, where

$a=50tan8^o$

$b=50tan14^o$

Therefore,

$h=50tan8^o+50tan14^o$

$h=50(tan8^o+tan14^o)$

$\boxed{h=50.25\ ft}$