unit 3 - study guide. questions 1 & 2 the pythagorean theorem states that the square of the...

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Unit 3 - Study Guide

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Question 3 Use what you know about the Pythagorean Theorem to label the sides of the following triangle. hypotenuse leg

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Page 1: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Unit 3 - Study Guide

Page 2: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Questions 1 & 2

The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

The Pythagorean Theorem can be represented by the equation a2 + b2 = c 2, where a and b are the length of the legs of the triangle, and c is the length of the hypotenuse.

Page 3: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 3

Use what you know about the Pythagorean Theorem to label the sides of the following triangle.

hypotenuseleg

leg

Page 4: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 4

Is a triangle with the lengths 7, 24, and 25 a right triangle. Why or why not. Show work to indicate how you got your answer.Use the Pythagorean Theorem to determine if this is a right triangle.72 + 242 = 252

49 + 576 = 625625 = 625The sum of the squares of the legs is equal to the square of the hypotenuse, so it is a right triangle.

Page 5: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 5

A football field is 360 feet by 45 feet. How long is the walk from one corner diagonally to the opposite corner?

360 ft

45 ft

452 + 3602 = c2

2025 + 129600 = c2

131625 = c2

362.8 ft = c

Page 6: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 6

Using the illustration below, what is the approximate height of the hot air balloon?

a2 + 13252 = 20002

a2 + 1755625 = 4000000

a2 = 2244375

a = 1498.1 ft

Page 7: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 7

A rectangle has a diagonal 25 inches long and a width of 6 inches. What is the length of the rectangle?

6 in25 in

62 + b2 = 252

36 + b2 = 625

b2 = 589

b = 24.3 in.

Page 8: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 8

Which of the following measures are valid measures of the sides of a right triangle? Explain your reasoning.

A. 3, 4, 7B. 5, 12, 13C. 20, 21, 28D. 12, 37, 34

5, 12, and 13 are valid measures of a right triangle because they form a Pythagorean Triple

Page 9: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 9A spider has taken up residence in a small cardboard box which measures 2 inches by 4 inches by 4 inches. What is the length, in inches, of a straight spider web that will carry the spider from the lower right front corner of the box to the upper left back corner of the box?

• =

Page 10: Unit 3 - Study Guide. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares

Question 10

A package is in the shape of a cube. The height if the package is 10 inches. What is the diagonal length of the package?

10 in =

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