You may use your calculator on this part of the test Draw tr

You may use your calculator on this part of the test. Draw triangles and show work whenever possible in order to receive credit. From a 200-fool observation tower on the coast, a Coast Guard officer sights a boat in difficulty. The angle of depression to the boat is 5 degree. How far is the A boat from the coast? To receive full credit, a properly labeled sketch is required. Round your answer to the nearest foot.

Solution

ALWAYS draw a picture if you are having trouble. Draw a vertical line - this is your tower. Label it 200 (the height of the tower). From the base of the tower, draw a line straight to the left. This is the distance to the boat, so label it x. Go ahead and close up the hypotenuse. Now you have a right triangle.

The angle of depression from the top of the tower = the angle of elevation of the boat = 5 degrees. This goes in the lower-lefthand corner of the triangle. Now you have an angle, and you have values for the opposite side, and the adjacent side. So which trig function uses opposite and adjacent? Tangent.

tan = opp/adj.
tan(5) = 200/x
xtan(5)=200
x=200/tan(5) = 2286 feet