Question

Suppose the sun casts a shadow off a 20-footbuilding. If the angle of elevation to the sun is 65°,how long is the shadow to the nearest tenth of afoot?20 feet6509.3 feet13.2 feet17.2 feet21.1 feet

Answer 1

The triangle formed by the system in the question is shown below:

The length of the shadow is represented by x.

We can use the Tangent Trigonometric ratio to solve for x.

The ratio is given as

$\tan \theta=\frac{\text{opp}}{\text{adj}}$

From the diagram above, we have the following parameters:

$\begin{gathered} \theta=65 \\ \text{opp }=20 \\ \text{adj }=x \end{gathered}$

Hence, we can substitute as

$\tan 65=\frac{20}{x}$

Solving for x, we have

$\begin{gathered} 2.145=\frac{20}{x} \\ \therefore \\ x=\frac{20}{2.145} \\ x=9.3\text{ feet} \end{gathered}$

The correct answer is the FIRST OPTION (9.3 feet).