Download Name - Garnet Valley School District

Algebra III Academic
Trigonometry
Pythagorean Theorem, Special Right Triangles and Right Triangle Trigonometry (Day 1)
SOH-CAH-TOA
These ratios are used to find missing parts of right triangles given a limited amount of information.
Sin  = Opposite leg to <
Hypotenuse
Cos  = Adjacent leg to <
Hypotenuse
Tan  = Opposite leg
Adjacent leg
Pythagorean Theorem States:_____________________________________________________________
Special Right Triangles:
30-60-90
45-45-90
Solve the right triangles that follow. (Find all side lengths and all angles)
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Example 6:
Find the value of x to the nearest tenth.
a.
b.
59
8
x
15
x
47
c.
d.
12
x
In  ABC, find a, b,
24
5
x
7
Angle of Elevation: _____________________________________________________________________
Angle of Depression: ____________________________________________________________________
Examples
1. A lighthouse keeper observes that there is a 3 angle of depression between the horizontal and the line
of sight to a ship. If the keeper is 19 m above the water, how far is the ship from shore?
2. Suppose you have been assigned the job of measuring the height of the local water tower. Climbing
makes you dizzy, so you decide to do the whole job at ground level. From a point 47.3 meters from the
base of the tower, you find that you must look up at an angle of 53° to see the top of the tower. How
high is the tower?
3. Standing across the street 50 feet from a building, the angle to the top of the
building is 40°. An antenna sits on the front edge of the roof of the building. The
angle to the top of the antenna is 52°. How tall is the building? How tall is the
antenna itself, not including the height of the building?
Algebra III Academic
Trigonometry
Pythagorean Theorem, Special Right Triangles and Right Triangle Trigonometry (Day 1)
Homework
Find the value of x using properties of special right triangles. Leave your answers in radical form.
1.
2.
10
15
45
60
x
3.
x
4.
30
14
12
60
x
x
5.
6.
60
18
x
45
x
18
7.
8.
11
12
x
60
45
x
Find the value of the variables. Round to the hundredth.
9. Find the value of x and y.
65
x = ________
8 cm
y = ______
x
y
10. Find the value of w and v.
w = ______
9 cm
v = ______
A
w
70
v
11. Find the value of x and y.
y
x
x = _______
y = ______
C
72
B
3 in
12. Your cat is trapped on a tree branch 6.5 meters above the ground. Your ladder is only 6.7 meters long. If
you place the ladder’s tip on the branch, what angle will the ladder make with the ground?
13. You must order a new rope for a flagpole. To find out what length of rope is needed, you observe that the
pole casts a shadow 11.6 meters long on the ground. When you look at the top of the pole, the angle of
elevation is 36°. How tall is the pole?
14. An airplane is at an elevation of 35000 feet when it begins its approach to an airport. Its angle of
depression is 6. Determine the distance between the airport and the point on the ground directly below the
airplane?