An observer 80 feet above the surface of the water measures an angle of 0 degrees 42 minutes to a distant ship. How many miles is the ship from the base of the lighthouse?
+128474 The angle of depression is .7 degrees. This means the observer is looking at .7 degrees below the horizontal.
The angle between horizontal and vertical = 90 degrees. So the remaining part of the angle is given by (90 -.7) = 89.3 degrees.
The distance the ship is from the lighthouse is the opposite side of this angle and the adjacent side is the height of the lighthouse.
Does that help??
+128474 So we know the angle of depression (42 minutes) = .7°. And we can use the following to find the distance the ship is from the lighthouse (call this x)
tan (90 - .7) = x / ht of lighthouse
tan( 89.3) = x / 80 ft
Multiply both sides by 80 ft
(80 ft.) tan (89.3) = x = about 6547.8 ft = about 1.24 miles
+128474 The angle of depression is .7 degrees. This means the observer is looking at .7 degrees below the horizontal.
The angle between horizontal and vertical = 90 degrees. So the remaining part of the angle is given by (90 -.7) = 89.3 degrees.
The distance the ship is from the lighthouse is the opposite side of this angle and the adjacent side is the height of the lighthouse.
Does that help??
