Question

Two guy wires, 17 m and 10 m in length, are fastened to the top of a TV tower from twopoints M and N on level ground. The angle of elevation of the longer wire is 28.1" (this meansangle M is 28.1").a) How tall is tower?b) How far apart are M and N?

Answer 1

Step 1

Given;

Step 2

A) How tall is the tower?

Using trigonometric ratio;

$\begin{gathered} sin\theta=\frac{opposite}{Hypotenuse} \\ sin(28.1)=\frac{opposite}{17} \\ opposite=\text{ length of tower} \\ length\text{ of tower=17sin\lparen28.1\rparen}\approx8m \end{gathered}$

B) How far apart are M and N

$\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ cos(28.1)=\frac{adjacent}{17} \\ adjacent=14.99615672 \end{gathered}$$10^2=8^2+x^2$$\begin{gathered} 10^2-8^2=x^2 \\ x=\sqrt{100-64} \\ x=\sqrt{36}=6 \end{gathered}$

Thus, the distance between M and N is;

$\begin{gathered} 6+14.99615672=20.99615672 \\ MN\approx21m \end{gathered}$

Answer;

$\begin{gathered} A)\text{ Approximately 8m} \\ B)\text{ Approximately 21m apart} \end{gathered}$