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Examples

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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
Use your calculator to approximate.
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
Use your calculator to approximate.
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
    your answer to the nearest tenth.

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
adj.
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.
    Round your answer to the nearest tenth.

5 miles
opp.
tan 19
Use correct ratio
adj.
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
9
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