Right Triangle Trigonometry

1
Right Triangle Trigonometry

• Section 4.3

2
Objectives

• Calculate any trigonometric function for an angle
  in a right triangle given two sides of the
  triangle.
• Calculate the length of the sides of a right
  triangle given the measure of an angle of a
  triangle.
• Solve word problems requiring right triangles and
  trigonometric functions.

3
Vocabulary

• angle of elevation
• angle of depression

4
Trigonometric Functions

• sin(x)
• cos(x)
• tan(x)

5
Trigonometric Functions

• csc(x)
• sec(x)
• cot(x)

6
For the triangle
y

• Find sin(x)
• Find cos(y)
• Find tan(x)
• Find cot(y)

3
x
5
7
For the triangle
y

• Find sec(x)
• Find csc(y)

3
x
5
8
Identities

• Cofunction Identities

• sin(x) cos(90-x)
• cos(x) sin(90-x)
• tan(x) cot(90-x)
• cot(x) tan(90-x)
• sec(x) csc(90-x)
• csc(x) sec(90-x)

9
For the triangle below, if BC 7 and the angle ß
60?, find all the missing angles and sides.
10
A plane if flying at an elevation of 27000 feet.
It is within sight of the airport and the pilot
finds that the angle of depression to the airport
is 25 degrees. Find the distance between the
plane and the airport.
11
A hot-air balloon is floating above a straight
road. To calculate their height above the
ground, the balloonists simultaneously measure
the angle of depression to two consecutive
mileposts on the road on the same side of the
balloon. The angles of depression are found to
be 23 degrees and 27 degrees. How high (in feet)
is the balloon?
12
The angle of elevation to the top of the Empire
State Building in New York is found to be 11
degrees from the ground at a distance of 1 mile
from the base of the building. Using this
information, find the height of the Empire State
Building.