Question

How would I do this one?

From a balloon 760 feet high, the angle of depression to the ranger headquarters is 89Á18'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Answer 1

First we would need to make a diagram, and from the given it would seem like it is a right triangle with the height as 760 ft. We have an angle given 89°18' which would need to be converted to degrees form, which is 89.3°.

Now we would need to look for the ground distance, meaning the adjacent of the triangle. Since we have been given the angle and the height (which is the opposite side from the angle) we use the trigonometric function cotangent.

760 Cot [(89.3)∘]= 9.29 ft, that is the answer.

Answer 2

The headquarters is 9 ft away from a point on the ground directly below the balloon .

Explanation:

The height of balloon is 760 ft and the angle of depression is 89°18' =
`89 (18)/(60) =89.3`°.

A right angled triangle is formed ( as shown in figure ) .Let x represent the distance of headquarters from a point on the ground directly below the balloon .

`Tan 89.3=(760)/(x)`

81.85 x= 760 .[ Tan 89.3= 81.85]

Dividing both sides by 81.85:

x= 9.3

Or x=9 ft ( rounded to nearest foot)

The headquarters is 9 ft away from a point on the ground directly below the balloon .