Download Notes – Angles of Elevation and Depression

Notes – Angles of Elevation and Depression
Many problems in daily life can be solved by using trigonometry. Often such problems involve an
angle of elevation or an angle of depression.
Angle of Elevation -- an angle formed by a ___________line and a line of sight to a point ______
the line.
airplane
angle of elevation
Angle of Depression -- an angle formed by a __________line and a line of sight to a point _____
the line.
angle of depres sion
_________ is the angle of elevation
_________ is the angle of depression
2
Caution: The angle of depression MAY NOT be
one of the angles in the triangle you are
solving. Instead it is the ___________ of one of
the angles in the triangle.
1
Example: An operator at the top of a lighthouse can sight the sailboat by lowering a telescope
through an angle of 3° from the horizontal. This angle is called the ____________________.
horizontal
Method #1 (Using the complement)
3
tan 87° =
lighthouse
20m
x
sailboat
horizontal
At the same time, a person in the
sailboat can sight the top of the
lighthouse by raising a telescope
through a 3° angle from the
horizontal. This angle is called the
_______________________.
Thus, the angle of depression
_________ the angle of elevation.
Method #2 (using the fact that angle of
depression & angle of elevation are =)
tan 3° =
Own Your Own
1. The angle of elevation from Point A to the top of a cliff is 38°. If Point A is 80 feet from the base of
the cliff, how high is the cliff?
2. A wheelchair ramp is 6 ft in length and makes a 4° angle with the ground. How many inches does
the ramp rise off the ground?
3. From the top of a tower, the angle of depression to a stake on the ground is 72°. The top of the
tower is 80 feet above the ground. How far is the stake from the foot of the tower?
4. A tree 40 feet high casts a shadow 59 feet long. Find the angle of elevation of the sun.
5. A ladder leaning against a house makes an angle of 60° with the ground. The foot of the ladder is
7 feet from the foundation of the house. How long is the ladder?
6. A diagonal path through a rectangular park is 600 ft long. One side of the park measures 350 ft.
a) How long is the other side of the park?
b) What angle does the diagonal path make
with the side whose length you found in part a?