Use trigonometry to find the measures of the sides of right triangles.

When using right triangles to solve problems, make sure you draw a diagram so you can accurately determine the sides, angles and useful trigonometric functions. Angle of elevation The angle between a horizontal line and the line of sight from the observer to an object at a higher level. Angle of depression The angle between a horizontal line and the line of sight form the observer to an object at a lower level.

1) The circus has arrived and the roustabouts must put up the main tent in a field near town. A tab is located on the side of the test 40 feet above the ground. A rope is tied to tent at this point and then the rope is placed around a stake on the ground. If the angle that the rope makes with the level ground is 52°15’, how long is the rope? What is the distance between the bottom of the tent and the stake?

2) The chair lift at a ski resort rises at an angle of 20.75° and attains a vertical height of 1200 feet. a) How far does the chair lift travel up the side of the mountain?

3) A regular hexagon is inscribed in a circle with diameter 26.6 centimeters. Find the apothem of the hexagon.

4) An observer in the top of a lighthouse determines that the angles of depression to two angles of depression to two sailboats directly in line with the lighthouse are 3.5° and 5.75°. If the observer is 125 feet above sea level find the distance between the boats.