Question

Mr A, used an app on his phone and measured the angle of elevation to the top of a mountain and found it to be 21°He then drove 4.5 miles closer to the mountain and then again measured that angle of the elevation now is 47° assuming he drove along a straight flat road, What is the height of the mountain?( round your answer to the nearest hundredth of a place and label appropriate units(

Answer 1

2.69 miles

1) Gathering the data, let's sketch that:

2) As we can see we have two triangles, so we can solve it using trigonometry.

So we can write that the height of the mountain is equal to the following trigonometric ratios (tangent):

`\begin{gathered} \tan \text{ (21) = }(h)/(4.5+x) \\ 0.3839(4.5+x)\text{ =h} \\ \tan \text{ (47) =}(h)/(x) \\ h=1.0723x \\ 0.3839(4.5+x)\text{ =h} \\ 1.72755+0.3839x=1.0723x \\ 1.72755\text{ =1.0723x-0.3839x} \\ 1.72755=0.6884x \\ x=(1.72755)/(0.6884) \\ x=2.509\approx2.51 \\ \text{Plugging into h=1.0723x} \\ h=1.0723(2.51) \\ h=2.691\approx2.69 \end{gathered}`

So the height of the mountain is approximately 2.69 miles