Chapter 9.4, Problem 35PS

Solution

To find: The drawing of a diagram to represent the given situation. At what angle should the firefighter set the ladder?

Hence, angle on which firefighter set the ladder is $53.13°$.

Given: height of fire truck ladder is 100 foot whose base is 10 feet above the ground. Distance between the ladder and burning building is 90 feet.Concept Used: $\sin \theta =\frac{oppositeside}{Hypotenuseside}$

Calculation:

Height of fire truck ladder is 100 foot whose base is 10 feet above the ground. Distance between the ladder and burning building is 90 feet.

Constructing a diagram on the given situation:

  

Now, from the figure:

  $\begin{array}{c}\sin \theta =\frac{PQ}{PS}\\ \sin \theta =\frac{80}{100}\\ \theta ={\sin }^{-1}(0.8)\\ \theta =53.1301024°\\ \theta =53.13°\end{array}$

Conclusion:

Hence, angle on which firefighter set the ladder is $53.13°$.