5.8 Problem Solving with Right Triangles Angle of elevation horizontal line of sight Angle of depression line of sight

Ex. 1: From a distance of 20 m from the base a lighthouse the angle of elevation to the top of a lighthouse is 38º. Determine the height of the lighthouse. 38º h h = 20 tan 38° h = 20 (0.7813) h = 15.6 The lighthouse is 15.6 m high. 20 m h

Example 2: A surveyor measures the distance from the base a tree as 13 m. If the angle of elevation to the top of the tree is 50°, determine the height of the tree. h = 13 tan 50° h = 15.5 The height of the tree is 15.5 m. h 50° 13 m

Example 3: The shadow cast by a building is 31 m. If the building is 52 m tall, determine the angle of elevation of the sun. tan  = The angle of elevation of the sun is 59.2°.  = tan – 1 (1.6774)  = 59.2° 52 m  31 m

Example 4: The angle of depression from an observation tower to a campfire is 3°. If the tower is 28 m tall, how far away from the base of the tower is the campfire? The campfire is 534 m from the tower. x  534 m 3° x 28 m 3°

26° Ex. 5: A ladder is leaning against a wall and makes an angle of 26º with the wall. If the ladder is 3 m long, how far up the wall does the ladder reach? 3 m x x = 3 cos 26° x = 3 (0.8988) x = 2.7 The ladder reaches 2.7 m up the wall.

Ex. 6: A local building code states that the maximum slope for a set of stairs is 68 cm rise for every 100 cm of run. What is the maximum angle at which the set of stairs can rise?  tan  = 0.68  = tan –  = 34.2º The maximum angle is 34.2º