Question

A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?

Answer 1

This is a problem on right triangle trigonometry. The hypotenuse is 60 feet and the unknown side is opposite the given 75-degree angle. Given these values, we will use the sine function. That is 
     $sin\left(75^{\circ} \right)=\frac{h}{60}$

     $h=60\cdot sin\left(75^{\circ} \right)=58\:feet$

The maximum height that the ladder can safely reach is closest to 58 feet.