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### Examples Find the sine, cosine and tangent of angles A, B. ... 9.6 Solving Right Triangles Author: Robert Spitz Last modified by: acalise2 Created Date: – PowerPoint PPT presentation

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Title: Examples

1
Examples
• Find the sine, cosine and tangent of angles A, B.
• Bonus find the sine of angle C.

A
13
Sin(A) 5/13 Sin(B) 12/13 Cos(A) 12/13
Cos(B) 5/13 Tan(A) 5/12 Tan(B)
12/5 Sin(C) 1
12
B
C
5
2
Right Triangle Trigonometry
• Geometry
• Mr. Calise

3
Ex. 2 Solving a Right Triangle (h)
• Solve the right triangle. Round decimals to the
nearest tenth.

25
You are looking for opposite and hypotenuse which
is the sin ratio.
Set up the correct ratio
Substitute values/multiply by reciprocal
Substitute value from table or calculator
13(0.4226) h
5.5 h
4
Ex. 2 Solving a Right Triangle (g)
• Solve the right triangle. Round decimals to the
nearest tenth.

25
You are looking for adjacent and hypotenuse which
is the cosine ratio.
Set up the correct ratio
Substitute values/multiply by reciprocal
Substitute value from table or calculator
13(0.9063) g
11.8 h
5
Using Right Triangles in Real Life
• Space Shuttle During its approach to Earth, the
space shuttles glide angle changes.
• A. When the shuttles altitude is about 15.7
miles, its horizontal distance to the runway is
about 59 miles. What is its glide angle? Round

6
Solution
Glide ? x
15.7 miles
• You know opposite and adjacent sides. If you
take the opposite and divide it by the adjacent
sides, then take the inverse tangent of the
ratio, this will yield you the slide angle.

59 miles
opp.
tan x
Use correct ratio
15.7
Substitute values
tan x
59
Key in calculator 2nd function, tan 15.7/59
14.9
? When the space shuttles altitude is about
15.7 miles, the glide angle is about 14.9.
7
B. Solution
Glide ? 19
h
• When the space shuttle is 5 miles from the
runway, its glide angle is about 19. Find the
shuttles altitude at this point in its descent.

5 miles
opp.
tan 19
Use correct ratio
h
Substitute values
tan 19
5
h
5
Isolate h by multiplying by 5.
5 tan 19
5
? The shuttles altitude is about 1.7 miles.
1.7 h
Approximate using calculator
8
Drill Find the height of the tree.
50 feet
40o
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