# Thread: problem solving with trig ratios

1. ## problem solving with trig ratios

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 13.2and theangle of elevation to the bottom of the tower is 8.3. Find the height of the hill.

2. ## Re: problem solving with trig ratios

Originally Posted by calmo11
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 13.2and 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:

$\frac hx=\tan(8.3^\circ)~\implies~x=\frac h{\tan(8.3^\circ)}$

$\frac{h+42}x=\tan(13.2^\circ)$

Sub in the term for x into the 2nd equation:

$\frac{h+42}{\frac h{\tan(8.3^\circ)}}=\tan(13.2^\circ)$

Solve for h.

I've got: $h \approx 69.1\ m$

3. ## Re: problem solving with trig ratios

Great! Thanks very much for your help

### A tower 42 m high stands on top of a hill. From a point some distance away from the hill , the angle of elevation of the top of the tower is 13.2° and the angle of elevation of the bottom of the tower is 8.3° . Find the height of the hill.

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