Question

A 40 foot Flag pole stands on the top of the hill. To measure the height of the hill a survey or standing at the base of the hill finds a measure of the angle of elevation of the top and bottom of the flag got to be 49.7 and 39.3 respectively. Find the height of the hill to the bottom of the nearest foot

Answer 1

Let h $=$ Height of the hill

And $h_o=$ Horizontal distance of Surveyor, S from the foot of the hill.

Tan $49.7=\frac{40+h}{h_o} \implies h_o=\frac{40+h}{Tan49.7}$

Tan $39.3=\frac{h}{h_o}\implies\>h_o=\frac{h}{Tan 39.3}$

$\frac{40+h}{Tan49.7}=\frac{h}{Tan39.3}$

$40$ tan $39.3+h\>$ tan $39.3=h$ tan $49.7$

$40$ tan $39.3=h($ tan $49.7-$ tan $39.3)$

$h=\frac{40\> tan\>39.3}{tan\>49.7\>-\>tan\>39.3}$

$=90.775ft$