Solve the problem.
-From a boat on the lake, the angle of elevation to the top of a cliff is $31 ^ { \circ } 5 ^ { \prime }$. If the base of the cliff is 666 feet from the boat, how high is the cliff (to the nearest foot)?
A) $401 \mathrm { ft }$
B) $414 \mathrm { ft }$
C) $411 \mathrm { ft }$
D) $404 \mathrm { ft }$

Question

Quizplus · Accepted Answer

To find the height of the cliff, we can use the tangent of the angle of elevation, which is the ratio of the opposite side (height of the cliff) to the adjacent side (distance from the boat to the base of the cliff). The tangent of $31^\circ 5'$ can be calculated or looked up in a trigonometry table. Using the formula $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, we have $\tan(31^\circ 5') = \frac{\text{height}}{666}$. Solving for the height gives us approximately 401 feet.

Solve the Problem 31∘5′31 ^ { \circ } 5 ^ { \prime }31∘5′

Solve the Problem $31 ^ { \circ } 5 ^ { \prime }$