Transcript Right Triangle Trigonometry

Right Triangle Trigonometry
Section 4.3
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.
Vocabulary
• angle of elevation
• angle of depression
Trigonometric Functions
• sin(x)
• cos(x)
• tan(x)
Trigonometric Functions
• csc(x)
• sec(x)
• cot(x)
For the triangle
y
• Find sin(x)
• Find cos(y)
3
x
5
• Find tan(x)
• Find cot(y)
For the triangle
y
• Find sec(x)
• Find csc(y)
3
x
5
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)
For the triangle below, if BC = 7
and the angle β = 60, find all the
missing angles and sides.
C
β
α
A
B
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.
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?
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.