PreCalculusTrig
posted by Chloe Mack .
A lighthouse keeper 100 feet above the water sees a boat sailing in a straight line directly toward her. As watches, the angle of depression to the boat changes from 25 degrees to 40. How far has the boat traveled during this time?

First, we draw a rectangle and label
the ver. sides 100ft and hor.(longer)
sides X ft. Then we draw a diag. from
upper left to lower rt. side forming a rt triangle. The angle of elevation = the angle of depression = 25deg.
Draw a 2nd line from upper left corner
to some point(near the center) on the
bottom hor. line forming an angle of
40deg with the hor. Label the 2 sections on the bottom line X1 and X2
(rt to lt).
tan25 = Y/X = 100/X,
X = 100 / tan25 = 214.45 ft.
tan40 = Y/X2 = 100/X2,
X2 = 100 / tan40 = 119.2ft.
X1 + X2 = X,
X1 + 119.2 = 214.5,
X1 = 214.5  119.2 = 95.3ft. = distance traveled.
Respond to this Question
Similar Questions

Precalculus
1. A man stands 12 feet from a statue. The angle of elevation from the eye level to the top of the statue is 30 degrees, and the angle of depression to the base of the statue is 15. How tall in the statue? 
math
A boat is spotted in the water with an angle of depression of 25° from the top of a lighthouse that is 89 feet tall. To the nearest foot, how far away is the boat from the base of the lighthouse 
Math(trig)
Peggy’s Cove Lighthouse, in Nova Scotia, is possibly the most photographed lighthouse in the world. From the observation deck, the angle of depression of a boat is 6º. How far is the boat from the lighthouse, to the nearest metre? 
PreCalculusTrig
A boat travels for 8 kilometers in a straight line from the dock. It is then sighted from a lighthouse which is 6.5 kilometers from the dock. The angle determined by the dock, the lighthouse(vertex), and the boat is 25 degrees. How … 
Math (Trig.)
A boat sailing from A to B travels in a straight line until the captain realizes he is off course. The boat is turned through an angle of 60 degrees, then travels another 10 km to B. The trip would have been 4 km shorter if the boat … 
math
From the top of a lighthouse 75 feet high, the cosine of the angle of depression of a boat out at sea is 4. To the nearest foot, how far is the boat from the base of the lighthouse? 
Please Help!!!!!!
From the top of a lighthouse 55ft above sea level, the angle of depression to a small boat is 11.3 degrees. How far from the foot of the lighthouse is the boat? 
Maths
From a point on a lighthouse 76 metres above sea level,the angle of depression of a fishing boat 28 degrees.How far is the boat from the foot of the lighthouse? 
Geometry
A lighthouse keeper in his observation tower 120 feet above the water sees a pontoon airplane and a small fishing boat. If the plane is directly above the boat, how far above sea level is the plane flying, rounded to the nearest foot? 
trig
Robert is standing on a cliff and looks down at an angle of depression of 62 degrees to look at a boat. The cliff is 76 feet high. How far is the boat from the cliff?