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
[tex]tan\theta =\frac{25}{53}[/tex]
[tex]tan(\theta +12.4)=\frac{h+25}{53}[/tex]
and we know [tex]tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}[/tex]
using above formula
[tex]tan(\theta +12.4)=\frac{tan\theta +tan(12.4)}{1-tan(\theta )tan(12.4)}[/tex]
[tex]\frac{h+25}{53}=\frac{\frac{25}{53}+0.219}{1-0.219\times \frac{25}{53}}[/tex]
[tex]0.896h+22.407=25+11.607[/tex]
h=15.848 ft
