Question

A 30-foot tree casts a 12-foot shadow as shown inthe picture.30 ftx12Find the angle of elevation to the nearest tenth.12.850°68.2°90°

Answer 1

Since the triangle has a right angle, we can conclude that the diagram is of a right triangle.

When dealing with right triangles, there are some useful formulas that are known as 'Trigonometric Identities'. There are a lot of them but we will need only one of those to solve the problem, that's the equation below:

$\tan (\theta)=\frac{O}{A}$

Where θ is the angle, O is the length of the opposite side to the angle, and A the adjacent side to the angle.

Therefore, in the case of our problem,

$\begin{gathered} \theta=x,O=30ft,A=12ft \\ \Rightarrow\tan (x)=\frac{30}{12}=2.5 \end{gathered}$

Solving for x, we get

$x=\tan ^{-1}(2.5)=1.1902\text{rad}$

And we can transform radians into degrees,

$\Rightarrow x\approx68.2$

Thus, the answer is the third option. 68.2°