4.3 Applications Involving Right Triangles

1
4.3 Applications Involving Right Triangles

• At the end of this lesson you will
  understand/apply
• sin and sin-1
• cos and cos-1
• tan and tan-1

What is the correct term for side AB, opposite
right ?C? What is the side opposite ?B? What is
the leg side adjacent to ?B? What is the side
opposite ?A? What is the leg side adjacent to ?A?
2
Three Trigonometric Ratios
Only for RIGHT triangles!!!!!
SOHCAHTOA or SohCahToa
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Why?
To solve triangles other than 30-60-90 or
45-45-90. Look on page 424 in your textbook
at the Table of Trigonometric Ratios. You have
the luxury of using a calculator! IMPORTANT
Your calculator must be in DEGREE mode.
4
Communicating
1. What happens to sin ?A as ?A increases? 2.
As ?A increases, what number is sin ?A
approaching? 3. Can you state/write a
generalization similar to above that describes
the relationship between the cos ?A and the
measure of ?A.
5
New Vocabulary
A
Angle of elevation The angle between an upward
line of sight and the horizontal.
?of elevation
P
H
P
H
?of depression
Angle of depression The angle between a
downward line of sight and the horizontal.
B
IMPORTANT These angles are between a line of
sight and the horizontal. Do NOT use the
vertical!
6
Using Trigonometric Ratios to Find a Missing Side
57?
x
Find missing side to nearest tenth.
10.8
37?
x
Find missing side to nearest tenth.
11
7
Using Trigonometric Ratios to Find a Missing Side
(cont.)
Find missing side to nearest tenth.
x
32?
13
8
Using Trigonometric Ratios to Find a Missing Angle
Find missing angle to nearest tenth.
??
5
4
13
12
9
Using Trigonometric Ratios to Find a Missing
Angle (cont.)
Find missing angle to nearest tenth.
7.7
14
10
Using Trigonometric Ratios to Solve a Word Problem
A boat is pulling a parasailer. The line to the
parasail is 800 feet long. The angle between the
line and the water is about 25?. (a) How high
is the parasailer? (b) How far back is the
parasailer from the boat?
800
25?