Chapter 10.6, Problem 5STP

Solve each exercise and enter your answer on the grid provided.

Suppose that you are watching the tree warden trim branches from a large tree in your yard. He has climbed up 15 meters and his assistant is holding a rope that will be used to guide the branch when it falls. To the nearest meter, how long is the rope?

To determine

To find the length of the rope.

Answer to Problem 5STP

  

Explanation of Solution

Given information:

The vertical distance of the rope from the ground is 15 m.

Angle made by the rope at top from an imaginary line parallel to ground is $55°$

Formula used:

Law of sines.

In any triangle, the ratio of side length to the sine of its opposite angle is the same for all three sides.

Calculation :

Angle made by the rope from ground is

  $55°\left[\text{alternate angles are equal}\right]$

Consider length of the rope be x meter.

  $\begin{array}{l}\frac{15}{\sin 55}=\frac{x}{\sin 90}\\ \frac{8}{0.82}=\frac{x}{1}\left[\sin 90=1,\sin 55=0.82\right]\\ x\approx 10\end{array}$

Length of the rope is approximately 10 meter.