Solve the problem.
-An angle above the horizontal is called an angle of elevation, and an angle below the horizontal is called an angle of depression. The pilot of a boat sees the light from a lighthouse at an angle of elevation of 13°. The light is on the shoreline, 350 feet above the dock. How far (to the nearest hundred feet) is the boat from the dock?
A) 1400 feet
B) 1500 feet
C) 2100 feet
D) 1600 feet

Question

Solve the problem.
-An angle above the horizontal is called an angle of elevation, and an angle below the horizontal is called an angle of depression.  The pilot of a boat sees the light from a lighthouse at an angle of elevation of 13°. The light is on the shoreline, 350 feet  above the dock. How far (to the nearest hundred feet) is the boat from the dock?
A) 1400 feet 
B) 1500 feet 
C) 2100 feet 
D) 1600 feet

Quizplus · Accepted Answer

We can draw a right triangle with the lighthouse at one vertex, the shoreline at another, and the boat at the third. The angle of elevation is 13°, so the complement of that angle (the angle between the shoreline and the horizontal) is 90° - 13° = 77°. We know that the height of the lighthouse above the dock is 350 feet, so we can use tangent to find the distance from the boat to the lighthouse:
tan(77°) = opposite/350
opposite = 350 tan(77°) ≈ 1508.4 feet
To the nearest hundred feet, the boat is 1500 feet from the dock.

Solve the Problem. -An Angle Above the Horizontal Is Called an Angle of an Angle