11.7 Angles of Elevation and Depression Notes
Warm Up:
Angles of Elevation and Depression
If an observer sights an object above, the angle between a horizontal line and his or her line of sight is called an
. If the line of sight is below the horizontal it is called the
Example 1: The angle of elevation of building A to building B is 250. The distance between the buildings is 21 meters.
Calculate how much taller Building B is than building A.
Example 2: A boat is 60 meters out to sea. Mary is standing on a cliff 80 meters high. What is the angle of depression
from the top of the cliff to the boat?
Example 3: Marty is standing on level ground when he sees a plane directly overhead. The angle of elevation of the
plane after it has travelled 25 km is 200. Calculate the altitude of the plane at this time.
Example 4: You sight a rock climber on a cliff at a 32o angle of elevation. The horizontal ground distance to the cliff is
1000 ft. Find the line of sight distance to the rock climber.
Example 5: An airplane pilots sights a life raft at a 26o angle of depression. The airplane’s altitude is 3 km. What is the
airplane’s surface distance d from the raft?
Example 6: A surveyor stands 200 ft from a building to measure its height with a 5-ft tall theodolite. The angle of
elevation to the top of the building is 35°. How tall is the building?
Example 7: An airplane flying 3500 ft above ground begins a 2° descent to land at an airport. How many miles from
the airport is the airplane when it starts its descent?
Example 8: A 6-ft man stands 12 ft from the base of a tree. The angle of elevation from his eyes to the top of the tree
is 40°.
Example 9: DIVING at a diving competition, a 6-foot-tall diver stands atop the 32-foot platform. The front edge of the
platform projects 5 feet beyond the ends of the pool. The pool itself is 50 feet in length. A camera is set up at the
opposite end of the pool even with the pool’s edge. If the camera is angled so that its line of sight extends to the top
of the diver’s head, what is the camera’s angle of elevation to the nearest degree?
Example 10: From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the tower to the
nearest meter?
Example 11: A ladder that is 20 ft is leaning against the side of a building. If the angle formed between the ladder and
ground is 75˚, how far is the bottom of the ladder from the base of the building?
Example 12: A ladder that is 20 ft is leaning against the side of a building. If the angle formed between the ladder and
ground is 75˚, how far is the bottom of the ladder from the base of the building?
Example 13: A kite is flying at an angle of elevation of about 55˚. Ignoring the sag in the string, find the height of the
kite if 85m of string have been let out.
Example 14: A 5.5 foot person standing 10 feet from a street light casts a 14 foot shadow. What is the height of the
streetlight?
Example 15: The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m
high, how far from the base of the tower is the boulder?
Example 16: Kate and Petra are on opposite sides of a tree. The angle of elevation to the top of the tree from Kate is
45o and from Petra is 65o. If the tree is 5 m tall, who is closer to the tree, Kate or Petra?
Example 17: Maryann is peering outside her window. From her window she sees her car and a bird hovering above
her car. The angle of depression of Maryann’s car is 200 whilst the angle of elevation to the bird is 400. If Maryann’s
window is 2m off the ground, what is the bird’s altitude at that moment?