A tower 42 metres high stands on top of a hill. From a point some distance fromthe base of the hill, the angle of elevation to the top of the tower is 13.2◦ and theangle of elevation to the bottom of the tower is 8.3◦. Find the height of the hill.
A tower 42 metres high stands on top of a hill. From a point some distance fromthe base of the hill, the angle of elevation to the top of the tower is 13.2◦ and theangle of elevation to the bottom of the tower is 8.3◦. Find the height of the hill.
Hello,
1. draw a sketch (see attachment)
2. You've got 2 right triangles. You'll get:
$\displaystyle \frac hx=\tan(8.3^\circ)~\implies~x=\frac h{\tan(8.3^\circ)}$
$\displaystyle \frac{h+42}x=\tan(13.2^\circ)$
Sub in the term for x into the 2nd equation:
$\displaystyle \frac{h+42}{\frac h{\tan(8.3^\circ)}}=\tan(13.2^\circ)$
Solve for h.
I've got: $\displaystyle h \approx 69.1\ m$