Finding Missing Angles and Sides of a Right Triangle

1
Finding Missing Angles and Sides of a Right
Triangle

• Adiel Cloud
• Tom Hansen
• Melanie Hatch
• Ben Clark

2
Introduction

• What is solving a right triangle?
• Finding missing angles
• Formula for Trig. Functions
• Finding missing sides
• Example Problem for class
• Summary
• Bibliography

3
What is solving a right triangle?

• Finding values of the unknown parts of a right
  triangle by using known values of other parts

4
Finding the missing angles.

• Because the total of the angles need to equal
  180, subtract the two given angles from 180.

?

• 180-30-90?

30

• ?60

5
Formula for Trig. Functions

• hyp
• ? opp
• adj
• Sin ? opposite csc ?
  hypotenuse
• hypotenuse
  opposite
• Cos ? adjacent sec ?
  hypotenuse
• hypotenuse
  adjacent
• Tan ? opposite cot ?
  adjacent
• adjacent
  opposite

6
Finding the missing sides

• Using the information given, use the sin of 60º
  and set it equal to opposite over hypotenuse,
  which is x/10.
• Sin60ºx/10
• X8.66

60º
10
x
7
Example Problem
A

• Solve ?ABC using the diagram and the given
  measurements.
• B24º, a8

c
b
B
C
a
8
Answer
A

• First, find the missing angle.
• Subtract 24 and 90 from 180 to find ?A
• 180-(2490) 66
• ?A 66

c
b
C
8
24
9
Answer (continued)
66

• Now, find the missing sides.
• To find side b
• Tan 24 b/8
• 8 Tan 24 b
• use calculator to find 8 Tan 24 ? 3.56
• b ? 3.56

c
b
C
8
24
10
Answer (concluded)
66

• To find side c
• Cos 24 8/c
• 8/Cos 24 c
• use calculator to find 8/ Cos 24 ? 8.76
• c ? 8.76

c
b
C
8
24
11
Summary

• To find missing angles of a right triangle,
  subtract two given angles from 180 or use sine,
  cosine, and tangent with a calculator.
• To find missing sides, use either the Pythagorean
  theorem, or sine, cosine, and tangent with a
  calculator.

12
Bibliography

• Littell, McDougal, and Larson, Boswell, Kanold,
  Stiff. Algebra 2. Evanston, Illinois A Houghton
  Mufflin Company, 2001.
• "Solving a Right Triangle." 2000. 5 February,
  2003. ltwww.education2000.com/demo/demo/botchtml/so
  lritri.htmgt.