Transcript 1 - iModules

What you will learn



How to evaluate inverse trigonometric functions
How to find missing angle measures
How to solve right triangles
1
Introduction
2
Sometimes when solving triangles, we know the
trigonometric value of an angle but not the angle.
When solving these problems, we need to use the inverse
of a trigonometric function (working backward from
the ratio to the angle measure).
Objective: Section 5-5 Solving Right Triangles
Definitions
3
The inverse of the basic trigonometric functions:
Arcsine = inverse of sine (sin-1)
Arccosine = inverse of cosine (cos-1)
Arctangent = inverse of tangent (tan-1)
Objective: Section 5-5 Solving Right Triangles
Example
4
sin x =
3 can be re-written as x = arcsin 3
2
2
The answer consists of all angles that have
of sine x.
Objective: Section 5-5 Solving Right Triangles
3
2
as the value
Example Problems
5
Solve each equation.
3
A. Sin x =

2
B. Cos x =
2

2
Objective: Section 5-5 Solving Right Triangles
C. Tan x = 1
More Examples
6

Evaluate each expression. Assume all angles are in
Quadrant I.
A.
6
tan(tan
)
11
B.
2
cos(arcsin )
3
1
Objective: Section 5-5 Solving Right Triangles
You Try
7
Evaluate each expression. Assume that all angles are in
Quadrant I.
A. tan(cos 1 4 )
5

B.
2
cos(arccos )
5
Objective: Section 5-5 Solving Right Triangles
Finding Angle Measures
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
F
If f = 17 and d = 32, find E.
d
E
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You Try! If d = 28 and f = 21, find F.
Objective: Section 5-5 Solving Right Triangles
e
f
D
Word Problem
9

A security light is being installed outside a loading dock. The
light is mounted 20 feet above the ground. The light must be
placed at an angle so that it will illuminate the end of the
parking lot 100 feet away. What should the angle of
depression be?
Objective: Section 5-5 Solving Right Triangles
Solving Right Triangles
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B
Solve the triangle described.
A. A = 33o, b = 5.8

a
c
A
B. a = 23, c = 45
Objective: Section 5-5 Solving Right Triangles
C
b
You Try
11
Solve each triangle described. Round to the nearest
tenth.
K
A. K = 40o, k = 26
j

l
B. j = 65, l = 55
Objective: Section 5-5 Solving Right Triangles
J
k
L
Homework
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Homework: page 309, 16-24 even, 28-32 even, 3640 even, 44
Objective: Section 5-5 Solving Right Triangles