From a balloon 1106 feet high, the angle of depression to the
ranger headquarters is 66 degrees 43'. how far is the headquarters
from a point on the ground directly below the balloon to the
nearest foot.

the distance from the headquarters from a point on the ground directly below the balloon is

175 feet

Step-by-step explanation:

The right angle triangle ABC formed is shown in the attached photo. C represents the position of the balloon.

A represents the position of the ranger headquarters.

x represents the distance from the headquarters from a point on the ground directly below the balloon.

1 minute = 0.0167 degrees

Converting 43' to degrees, it becomes 43 × 0.0167 = 0.7181

Angle A = 66 + 0.7181 = 66.7181 degrees.

We would apply trigonometric ratio

Tan # = opposite side/ adjacent side

# = 66.7181 degrees.

opposite side = 1106

Tan 66.7181 = 1106/x

6.324 = 1106/x

x = 1106/6.324

x = 175 feet

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step-by-step explanation:

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