solving right triangles 9.6 chapter 9 right triangles and trigonometry section 9.6 solving right...

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Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

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Page 1: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

Chapter 9Right Triangles and Trigonometry

Section 9.6

Solving Right Triangles

SOLVE RIGHT TRIANGLES

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

Page 2: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

Solving Right TrianglesCONCEPT

SUMMARY

SOLVE RIGHT TRIANGLES

To Solve A Right Triangle: Determine the measure of all three angles and the length of all three sides.

a

C

B

ab

c

1. Three Angles

A, B, C

2. Three Sides

• a, b, c

Page 3: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

Example 1 Given 1 Side and 1 Angle

Example 2 Given 2 Sides

Example 3 Solving Real Life Problems

Homework

SOLVE RIGHT TRIANGLES

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

Page 4: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 1 Side, 1 Angle

X & Y are Complements

mX + mY =90

71 + mY =90

mY = 19

1910.4

30.3

Page 5: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 1 Side, 1 Angle

Find AB, AC, mA

1952tan

AB

AB52tan19

AB 24.319

AC19

52cos

19)52(cos AC

52cos19AC

mA + mC = 90

mA + 52 = 90

mA = 3830.861AC

Page 6: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

mN = 55

sin359

MN MN 5.162

cos359

LM LM 7.372

Solving a Right Triangle Given 1 Side, 1 Angle

Page 7: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 2 Sides

Page 8: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 2 Sides

=12

125

tan 1B 22.62

mA + mB = 90

mA + 33.69 =90

mA 67.38

Page 9: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 2 Sides

Use the Pythagorean theorem to find XZ

(XZ)2 + 142 = 252

(XZ)2 + 196 = 225

(XZ)2 = 29

29XZ

Page 10: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 2 Sides

Need to find X

2514

sin X

X

2514

sin 1

mX 34.06

mX + mY = 90

34.06 + mY = 90

mY 55.94

Page 11: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Solving Right Triangles9.6

SOLVE RIGHT TRIANGLES

Solving a Right Triangle Given 2 Sides

340 2 85 18.439ML

1 12tan 40.601

14m M

49.399m L

Page 12: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

CIRCUS ACTS At the circus, a person in the audience watches the high-wire routine. A 5-foot-6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member from the base of the platform, if the angle of elevation from the audience member’s line of sight to the top of the acrobat isMake a drawing.

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

Page 13: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Since QR is 25 feet and RS is 5 feet 6 inches or 5.5 feet, QS is 30.5 feet. Let x represent PQ.

Multiply both sides by x.

Divide both sides by tan

Simplify.

Answer: The audience member is about 60 feet from the base of the platform.

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

Page 14: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

SHORT-RESPONSE TEST ITEM A wheelchair ramp is 3 meters long and inclines at Find the height of the ramp to the nearest tenth centimeter.

Solve the Test ItemMethod 1The ground and the horizontal level with the platform to which the ramp extends are parallel. Therefore,

since they are alternate interior angles.

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

Page 15: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

Answer: The height of the ramp is about 0.314 meters,

Mulitply each side by 3.

Simplify.

Y

W

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS

Page 16: Solving Right Triangles 9.6 Chapter 9 Right Triangles and Trigonometry Section 9.6 Solving Right Triangles SOLVE RIGHT TRIANGLES USE RIGHT TRIANGLES TO

SHORT-RESPONSE TEST ITEM A roller coaster car is at one of its highest points. It drops at a angle for 320 feet. How high was the roller coaster car to the nearest foot before it began its fall?

Answer: The roller coaster car was about 285 feet above the ground.

USE RIGHT TRIANGLES TO SOLVE REAL LIFE PROBLEMS