Posted by **Abby** on Thursday, February 18, 2010 at 3:22pm.

1) Find the angle of depression from the top of a lighthouse 250 feet above water level to the water line of a ship 2 miles off shore.

arc tan 10560/250 = 88.64 ft

Is this correct?

2) A passenger is in an airplane flying at n altitude of 10 kilometers sees two towns directly to the left og the plane. Tha angles of depression to the towns are 28 degrees and 55 degrees. How far apart are the towns?

I know that 90-55-28 = 7 and then take the inverse of tan so arc tan (&) = 81.81. Is that correct so far? I do not know what to do after this.

- Math -
**drwls**, Thursday, February 18, 2010 at 3:39pm
1) No. They want an answer in degrees, not in feet. The answer is arctan250/10560= 1.36 degrees.

The curvature of the earth has been neglected. It is unimportant over a two mile distance.

2) Wrong again. Let the distances to the two towns be X1 (closest) and X2 (farthest).

You want to know X2 - X1.

X2 = 10 km/tan28

X1 = 10 km/tan55

You can solve for both X2 and X1 if you wish. Or use

X2 - X1 = 10 km*[1/tan28 - 1/tan55]

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