Question

A statue is mounted on top of a 21 foot hill. From the base of the hill where you are standing is 57feet and the statue subtends an angle of 7.1 degrees to where you are standing. Find the height of the statue

Answer 1

We will have situation as shown in figure in attachment.

Here OH is the hill of height 21 feet.

Statute is HS, so lets its height be h, so HS = h

Distance OA = 57 feet, observer distance from base of hill

Then ∠HAS = 7.1° (angle subtended by statue HS at point A)

First we wil find ∠OAH in right ΔOAH

so let ∠OAH be Ф

We will use $tanФ =\frac{opposite-side}{adjacent -side} = \frac{OH}{OA}$

$tanФ =\frac{21}{57}$

so Ф $= tan^-1( \frac{21}{57} )$

Ф = 20.22°

Now in right ΔOAS, we have

∠OAS = Ф + 7.1° = 20.22° +7.1° = 27.32°

so tan (27.32°) = $\frac{OS}{OA} =\frac{21+x}{57}$

$0.516581 =\frac{21+x}{57}$

Now we will solve for x here

So multiply both sides by 57

$0.516581 \times 57 =\frac{21+x}{57}\times 57$

29.445117 =21 + x

29.445117 -21 =21 + x -21

8.445 = x

So height of statue is 8.45 feet.