Question

A statue is mounted on top of a 25 foot hill. From the base of the hill to where you are standing is 53 feet and the statue subtends an angle of 12.4° to where you are standing. Find the height of the statue.

Answer 1

Answer:15.848 ft

Explanation:

Given Height of hill is 25 foot

and distance between Hill foot and feet is 53 feet

angle subtended by 12.4^{\circ}[/tex]

From diagram

`tan\theta =(25)/(53)`

`tan(\theta +12.4)=(h+25)/(53)`

and we know
`tan(A+B)=(tanA+tanB)/(1-tanAtanB)`

using above formula

`tan(\theta +12.4)=(tan\theta +tan(12.4))/(1-tan(\theta )tan(12.4))`

`(h+25)/(53)=((25)/(53)+0.219)/(1-0.219* (25)/(53))`

`0.896h+22.407=25+11.607`

h=15.848 ft