Chapter 12.8, Problem 7P

To determine

Find the height of the flagpole.

Answer to Problem 7P

13.16 meters.

Explanation of Solution

Given:

From the top of a building 10 m tall, the angle of elevation to the top of a flagpole is $11°$ .At the base of the building, the angle of elevation to the top of the flagpole is $39°$ .

Formula Used:

Law of Cosine :

  $a^2=b^2+c^2-2bc\cos A$

Law of Sine:

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

  

Calculation:

Represent the situation :

  

We need to find x.

Use Law of Sine in the upper triangle:

  $\begin{array}{l}\frac{\sin 101°}{y}=\frac{\sin 28°}{10}\\ \Rightarrow y=10\cdot \frac{\sin 101°}{\sin 28°}\mathrm{.................}[\text{multiply each side by }\frac{10y}{\sin 28°}]\\ \Rightarrow y\approx 20.90\text{ m}\end{array}$

Use the definition of Sine in the lower triangle:

  $\begin{array}{l}\sin \theta =\frac{\text{length of the opposite side to }\theta }{\text{length of the hypotenuse}}\\ \Rightarrow \sin 39°=\frac{x}{20.90}\\ \Rightarrow x=20.90(\sin 39°)\mathrm{........................}[\text{multiply each side by 20}\text{.90]}\\ \Rightarrow x=13.16\text{ m}\end{array}$

So, the height of the flagpole is 13.16 meteres.