Section 8-7 Applications of Right Triangle Trigonometry

Suppose an operator at the top of a lighthouse sights a sailboat on a line that makes a 2° angle with a horizontal line. The angle between the horizontal and the line of sight is called an angle of _______________. At the same time, a person in the boat must look 2° above the horizontal to see the tip of the lighthouse. This is an angle of _______________. depression elevation

Examples: 1. When the sun’s angle of elevation is 38°, a building casts a shadow of 45 m. How high is the building? 45 m 38° x 1

3. From the top of a lighthouse 20 m high, a sailboat is sighted having an angle of depression of 4°. How far from the lighthouse is the boat? 1 y(tan 4°) = 20 4° tan 4° y 20

2. Draw a diagram showing a person who is 1.5 m tall standing 20 m from the base of a building. Also show that the person sights the top of the building with an angle of elevation of 58°. Find the height of the building. 1.5 m 20 m 1.5 m z 58° 1 32 m m 33.5 m

HOMEWORK: page 318 #2-10 even