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# From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. If the distance between the radio antenna and the library is 1.3 mls, how many miles high is the balloon?

May 13, 2016

I found $0.8 m l s$

#### Explanation:

We could use trigonometry, although I am not sure you know about it...!
Anyway, using trigonometry we have that the height of the baloon $h$ can be found as:
$\frac{1.3}{h} = \tan \left({57}^{\circ}\right)$
where $\tan$ is the trigonometric ratio known as Tangent .
We can use a scientific calculator to find that:
$\tan \left({57}^{\circ}\right) = 1.5398 \approx 1.5$
so we get:
$\frac{1.3}{h} = 1.5$
rearranging:
$h = \frac{1.3}{1.5} = 0.8 m l s$

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