Astatue is mounted on top of a 21 foot hill. from the base of the hill to where you are standing is 57feet and the statue subtends an angle of 7.1° to where you are standing. find the height of the statue.

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

so

Ф = 20.22°

Now in right ΔOAS, we have

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

so tan (27.32°) =

Now we will solve for x here

So multiply both sides by 57

29.445117 -21 =21 + x -21

8.445 = x

So height of statue is 8.45 feet.

its a straight line parallel to the time axis