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.

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- Mar 23rd 2014, 03:20 AMcalmo11problem 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 13.2◦ and theangle of elevation to the bottom of the tower is 8.3◦. Find the height of the hill.

- Mar 23rd 2014, 05:50 AMearbothRe: problem solving with trig ratios
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 AMcalmo11Re: problem solving with trig ratios
Great! Thanks very much for your help :)