Question

A statue is mounted ontop of a 16 foot hill. Fromthe base of the hill towhere you are standingis 77 feet and the statuesubtends an angle of13.2° to where you arestanding. Find the heightof the statue.16 ft77 ft13.2°

Answer 1

Given:

• Height of hill = 16 feet

,

• Distance from you to the base of the hill = 77 feet

,

• Angle the hill subtends = 13.2 degrees

Let's find the height of the statue.

Since the statue subtends an angle of 13.2 degrees to where you are standing, let's find the distance from you to the statue using the trigonometric ratio formula for tangent:

`tan\theta=(opposite)/(adjacent)`

Where:

Opposite = 16 ft

Adjacent side = 77

Angle of elevation = θ

Thus, we have:

`\begin{gathered} tan\theta=(16)/(77) \\ \\ Take\text{ the tan inverse of both sides:} \\ \\ \theta=tan^(-1)((16)/(77)) \\ \\ \theta=11.74^o \end{gathered}`

Now, also apply the trigonometric ratio formula for tangent to find the total height of the hill and the statue:

`\begin{gathered} tan(13.2+11.74)=(x)/(77) \\ \\ tan(29.94)=(x)/(77) \\ \\ x=77tan29.94 \\ \\ x=35.81\text{ ft} \end{gathered}`

The height of the statue will be:

h = 35.81 - 16 = 19.81 ft

Therefore, the height of the statue is 19.81 feet.

• ANSWER:

19.81 feet.