Question

the angle of elevation to the top of a flagpole measured by a digital protractor is 57.1° from a point on the ground 68 feet away from its base. find the height of the flagpole. the height of the flagpole is approximately 105.00 ft. (do not round until the final answer. then round to two decimal places as needed.)

Explanation:

Step1: Use the tangent function

In a right - triangle (formed by the flagpole, the ground, and the line of sight), the tangent of an angle of elevation \(\theta\) is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 57.1^{\circ}\), the adjacent side \(x = 68\) feet, and the opposite side \(h\) is the height of the flagpole. So, \(\tan(57.1^{\circ})=\frac{h}{68}\).

Step2: Solve for \(h\)

Multiply both sides of the equation \(\tan(57.1^{\circ})=\frac{h}{68}\) by \(68\). We get \(h = 68\times\tan(57.1^{\circ})\).
Using a calculator, \(\tan(57.1^{\circ})\approx1.544\). Then \(h=68\times1.544 = 105.0\) (rounded to two decimal places).

Answer:

The height of the flagpole is approximately \(105.00\) ft.