Question

a certain flagpole that is 298 feet tall casts a shadow 136 feet long. find the angle of elevation of the sun.

the suns angle of elevation is \\(\square^{\circ}\\).
(round to the nearest degree as needed.)

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height of the flagpole is the opposite side (\(opp = 298\) ft) and the length of the shadow is the adjacent side (\(adj = 136\) ft) to the angle of elevation \(\theta\). We use the tangent function, \(\tan(\theta)=\frac{opp}{adj}\).
So, \(\tan(\theta)=\frac{298}{136}\)

Step2: Calculate the angle

First, compute \(\frac{298}{136}\approx2.1912\). Then, take the arctangent (inverse tangent) of this value to find \(\theta\). Using a calculator, \(\theta = \arctan(2.1912)\).
Calculating this, we get \(\theta\approx65.5^\circ\), which rounds to \(66^\circ\) when rounded to the nearest degree.

Answer:

\(66\)