Question

Two people decide to estimate the height of a flagpole. One person positions himself due north of the pole and the other person stands due east of the pole. If the two people are the same distance from the pole and 27 feet from the other, find the height of the pole if the angle of elevation from the ground to the top of the pole at each person's position is 54 degrees. Round your answer to the nearest whole number

Answer 1

Answer:

$h_{pole}=30ft$

Explanation: We have to find the height of the pole, which is just an opposite side of a triangle, we would have to resort to the pythagorean theorem and one of the trigonometric ratios, this is done as follows:

$\begin{gathered} \text{ Base is determined through pythagorean theorem:} \\ \Rightarrow a^2+b^2=c^2\rightarrow a=b \\ \therefore\rightarrow \\ 2a^2=27^2\Rightarrow a=b=\frac{27}{\sqrt[]{2}}=\frac{27\sqrt[]{2}}{2} \\ \end{gathered}$

Height of the pole:

$\begin{gathered} \tan (57^{\circ})=\frac{Opposite\text{ }}{\text{Adjacent}}=\frac{h}{b}=\frac{h}{(\frac{27\sqrt[]{2}}{2})} \\ \tan (57^{\circ})=\frac{2h}{27\sqrt[]{2}}\rightarrow h=\frac{27\sqrt[]{2}}{2}\tan (57^{\circ})=\frac{27\sqrt[]{2}}{2}\times(1.54)=29.40\cong30 \\ \therefore\rightarrow \\ h_{pole}=30ft \end{gathered}$