Question

determining an angle of elevation
a tree that is 14 feet tall casts a shadow that is 30 feet long. find the angle of elevation from the tip of the shadow to the top of the tree. round to the nearest degree.

Explanation:

Step1: Identify the right - triangle relationship

We have a right - triangle where the height of the tree is the opposite side ($a = 14$) and the length of the shadow is the adjacent side ($b = 30$) with respect to the angle of elevation $\theta$. We use the tangent function $\tan\theta=\frac{a}{b}$.
$\tan\theta=\frac{14}{30}$

Step2: Calculate the value of the tangent

$\tan\theta=\frac{14}{30}\approx0.4667$

Step3: Find the angle

We know that $\theta=\arctan(0.4667)$. Using a calculator, $\theta=\arctan(0.4667)\approx25^{\circ}$

Answer:

$25^{\circ}$