Question

A guy wire makes a 65° angle with the ground. walking out 37 feet further from the tower, the angle of elevation to the top of the tower is 39°. find the height of the tower, rounded to the nearest whole foot.

Answer 1

Let's call the height of the tower $h$ and the distance from the 65 degree angle to the base of the tower $d$.

We get two equations:

$\tan 65^\circ = \dfrac h d$

$\tan 39^\circ = \dfrac{h}{d+37}$

$h = d \tan 65^\circ = (d+37) \tan 39^\circ$

$d(\tan 65 - \tan 39) = 37 \tan 39$

$d = \dfrac{37 \tan 39}{\tan 65 - \tan 39}$

$h = d \tan 65 = \dfrac{37 \tan 39 \tan 65}{\tan 65 - \tan 39}$

$h \approx 48.1 \textrm{ feet}$

Answer: 48