Download Complementary Angles

GSE Geometry
Unit 3 –Right Triangle Trigonometry
3.5 – Notes & Practice
Name: ________________________________________________ Date: _______________________
Trig Application NOTES
Angle of Elevation & Angle of Depression
1. Classify each angle as an angle of elevation or
depression:
angle of
2. Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of
elevation to the nearest degree? (1 miles = 5280 feet)
300 ft
x
2miles
3. A 75 foot building casts an 82 foot shadow. What is the angle that the sun hits the
building? Round to the nearest degree.
x
75 ft
82 ft
4. A boat is sailing and spots a shipwreck 650 feet below the water. A diver jumps from
the boat and swims 935 feet to reach the wreck. What is the angle of depression
from the boat to the shipwreck, to the nearest degree?
x
650 ft
935 ft
GSE Geometry
Unit 3 –Right Triangle Trigonometry
3.5 – Notes & Practice
5. A construction worker leans his ladder against a building making a 60 angle with
the ground. If his ladder is 20 feet long, how far away is the base of the ladder from
the building to the nearest tenth?
20 ft
600
x
Complementary Angles
The complementary angles of a right triangle are the two non-right angles.
The sine of one angle is equal to the cosine of the other non-right angle.
Example: The sine of 42° =
2
3
2
and the cosine of 48° = .
3
𝟕
1. Angles A and B are complementary angles in a right triangle. The value of tan A is .
𝟐𝟒
What is the value of cos B?
A
C
B
𝟒
2. Angles A and B are complementary angles in a right triangle. The value of tan A is .
𝟑
What is the value of cos B?
A
C
C
GSE Geometry
Unit 3 –Right Triangle Trigonometry
3.5 – Notes & Practice
𝟖
3. Angles X and Y are complementary angles in a right triangle. The value of sin X = .
𝟏𝟕
Find the cos and tan of X and the sin, cos, and tan of Y.
𝟓
4. Angles X and Y are complementary angles in a right triangle. The value of sin X = .
𝟏𝟑
Find the cos and tan of X and the sin, cos, and tan of Y.
5. If the value of sin 23o = 0.39, then the cos _____ = 0.39?
6. If the value of sin 37o = 0.60, then the cos _____ = 0.60?