Solve the problem.
-A 33 -foot ladder is leaning against the side of a building. If the ladder makes an angle of $23 ^ { \circ } 46 ^ { \prime }$ with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.
A) $3.93 \mathrm { ft }$
B) $19 \mathrm { ft }$
C) $14.6 \mathrm { ft }$
D) $13.3 \mathrm { ft }$

Question

Quizplus · Accepted Answer

To find the distance from the base of the building to the bottom of the ladder, use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 23^\circ 46'$ and the hypotenuse is 33 ft. Solving for the opposite side gives: $\sin(23^\circ 46') = \frac{x}{33}$. Solving for $x$ gives approximately 13.3 ft.

Solve the Problem 23∘46′23 ^ { \circ } 46 ^ { \prime }23∘46′

Solve the Problem $23 ^ { \circ } 46 ^ { \prime }$