CPM Homework Help : INT2 Problem 5-46

To paint a house, Travis leans a ladder against the wall. If the ladder is $16$ feet long and it makes contact with the house $14$ feet above ground, what angle does the ladder make with the ground? Draw a diagram of this situation and show all work.

Hint:

A right triangle with a leg of 14 ft and hypotenuse of 16 ft. The angle, theta, is opposite the 14 foot side.

Step 1:

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

$\text{sin}\theta \ =\frac{14\text{ ft}}{16\text{ ft}}$

Step 2:

$\theta \ = \text{ sin}^{-1}\left(\frac{14\text{ ft}}{16\text{ ft}} \right )$

Answer:

$θ\approx61^\circ$