# problem solving with trig ratios

• Mar 23rd 2014, 03:20 AM
calmo11
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.
• Mar 23rd 2014, 05:50 AM
earboth
Re: problem solving with trig ratios
Quote:

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:

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

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

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: $\displaystyle h \approx 69.1\ m$
• Mar 23rd 2014, 06:26 AM
calmo11
Re: problem solving with trig ratios
Great! Thanks very much for your help :)