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

Step-by-step 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

$tan\theta =\frac{25}{53}$

$tan(\theta +12.4)=\frac{h+25}{53}$

and we know $tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}$

using above formula

$tan(\theta +12.4)=\frac{tan\theta +tan(12.4)}{1-tan(\theta )tan(12.4)}$

$\frac{h+25}{53}=\frac{\frac{25}{53}+0.219}{1-0.219\times \frac{25}{53}}$

$0.896h+22.407=25+11.607$

h=15.848 ft