Step: 1

[Apply Pythagorean theorem.]

Step: 2

[Subtract d ^{2} from both sides.]

Step: 3

[Substitute l and d .]

Step: 4

= 400 - 144

[Apply exponents and simplify.]

Step: 5

= 256

Step: 6

⇒ h = 256

[Take square root of both sides.]

Step: 7

= 16

Step: 8

Therefore, the height of the pole is 16 feet.

Correct Answer is : 16 feet

Step: 1

Let s be the side of the square garden and d be the distance Justin walked.

Step: 2

All the angles of a square are right angles. So, the diagonal of the square will be the hypotenuse of the right triangle formed by two adjacent sides and the diagonal.

Step: 3

[Apply Pythagorean theorem.]

Step: 4

[Substitute s = 16.]

Step: 5

[Apply exponents and simplify.]

Step: 6

[Take square root on both sides.]

Step: 7

The total distance Justin walked is 16.97 ft.

Correct Answer is : 16.97 ft

Step: 1

The length of the ladder l = 10 feet.

Step: 2

The distance from the foot of the ladder to the wall, d = 6 feet.

Step: 3

Let h be the height of the wall.

Step: 4

[Write Pythagorean theorem.]

Step: 5

[Subtract d ^{2} from both sides.]

Step: 6

= 10^{2} - 6^{2}

[Substitute l and h .]

Step: 7

= 100 - 36

[Apply exponents and simplify.]

Step: 8

= 64

Step: 9

[Take square root of both sides.]

Step: 10

= 8

Step: 11

Height of the wall = 8 feet.

Correct Answer is : 8 feet

Step: 1

Let s be the side of the square garden and d be the distance Jim walked.

Step: 2

All the angles of a square are right angles. So, the diagonal of the square will be the hypotenuse of the right triangle formed by two adjacent sides and the diagonal.

Step: 3

[Apply Pythagorean theorem.]

Step: 4

[Substitute s = 25.]

Step: 5

[Apply exponents and simplify.]

Step: 6

[Take square root on both sides.]

Step: 7

The total distance Jim walked is 35.35 ft.

Correct Answer is : 35.35 ft

Step: 1

Let h be the height of the pole.

Step: 2

[Apply Pythagorean theorem.]

Step: 3

[Subtract d ^{2} from both sides.]

Step: 4

[Substitute l and d .]

Step: 5

= 676 - 100

[Apply exponents and simplify.]

Step: 6

= 576

Step: 7

[Take square root of both sides.]

Step: 8

= 24

Step: 9

The height of the pole is 24 feet.

Correct Answer is : 24 feet

Step: 1

Draw the figure using the data in the question.

Step: 2

Length of the kite string = hypotenuse of a right triangle = 150 ft.

Step: 3

Distance between Wilma and the stake = One leg of the triangle = 90 ft.

Step: 4

Let height of the kite = another leg of the triangle = x ft.

Step: 5

90^{2} + x ^{2} = 150^{2}

[Apply Pythagorean theorem.]

Step: 6

8100 + x ^{2} = 22500

Step: 7

[Subtract 8100 from each side.]

Step: 8

[Take square roots on both sides.]

Step: 9

Height of the kite = 120 ft.

Correct Answer is : 120 ft.

Step: 1

Let h be the height of the pole.

Step: 2

[Apply Pythagorean theorem.]

Step: 3

[Subtract d ^{2} from both sides.]

Step: 4

[Substitute l and d .]

Step: 5

= 400 - 144

[Apply exponents and simplify.]

Step: 6

= 256

Step: 7

[Take square root on both sides.]

Step: 8

= 16

Step: 9

The height of the pole is 16 feet.

Correct Answer is : 16 feet

Step: 1

Let h be the height of the pole.

Step: 2

[Apply Pythagorean theorem.]

Step: 3

[Subtract d ^{2} from both sides.]

Step: 4

[Substitute l and d .]

Step: 5

= 100 - 36

[Apply exponents and simplify.]

Step: 6

= 64

Step: 7

[Take square root of both sides.]

Step: 8

= 8

Step: 9

The height of the pole is 8 feet.

Correct Answer is : 8 feet

Step: 1

Let s be the side of the square garden and d be the distance Latif walked.

Step: 2

All the angles of a square are right angles. So, the diagonal of the square will be the hypotenuse of the right triangle formed by two adjacent sides and the diagonal.

Step: 3

[Use Pythagorean theorem.]

Step: 4

[Substitute s = 25.]

Step: 5

[Simplify.]

Step: 6

[Take square root on both sides.]

Step: 7

Hence, the total distance Latif walked is 35.35 m.

Correct Answer is : 35.35 m

Step: 1

Let s be the side of the square garden and d be the distance Chris walked.

Step: 2

Step: 3

[Apply Pythagorean theorem.]

Step: 4

[Substitute s = 27.]

Step: 5

[Simplify.]

Step: 6

[Take square root on both sides.]

Step: 7

The total distance Chris walked is 38.18 ft.

Correct Answer is : 38.18 ft

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