Solve the problem.
-From a balloon 839 feet high, the angle of depression to the ranger headquarters is $77 ^ { \circ } 18 ^ { \prime }$. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?
A) $179 \mathrm { ft }$
B) $184 \mathrm { ft }$
C) $194 \mathrm { ft }$
D) $189 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The angle of depression is the angle between the horizontal and the line of sight to the object. In this case, the angle of depression is $77 ^ { \circ } 18 ^ { \prime }$. The height of the balloon is 839 feet. We can use the tangent function to find the distance from the balloon to the ranger headquarters.$$\tan 77 ^ { \circ } 18 ^ { \prime } = \frac { 839 } { x }$$$$x = \frac { 839 } { \tan 77 ^ { \circ } 18 ^ { \prime } } \approx 189$$Therefore, the distance from the balloon to the ranger headquarters is approximately 189 feet.

Solve the Problem 77∘18′77 ^ { \circ } 18 ^ { \prime }77∘18′

Solve the Problem $77 ^ { \circ } 18 ^ { \prime }$