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Use the Pythagorean theorem to find the length of the unknown side of the right triangle

Question : Use the Pythagorean theorem to find the length of the unknown side of the right triangle : 2163586

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the Pythagorean theorem to find the length of the unknown side of the right triangle. Give an exact answer.

1)

A) 20

B) 14

C) 19

D) 11

2)

A) 25

B) 20

C) 18

D) 24

3)

A) 57

B) √(57)

C) √(15)

D) √(71)

4)

A) 5

B) √(5)

C) 13

D) √(13)

5)

A) 25√(5)

B) 10√(5)

C) 25

D) 5√(5)

Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse.

6) a = 15, b = 20

A) 24

B) 18

C) 25

D) 13

7) a = 9, c = 15

A) 15

B) 14

C) 11

D) 12

8) a = √(3), c = 5

A) 22

B) 4

C) √(22)

D) 2√(7)

9) a = 6, b = 21

A) 159

B) 135

C) 3√(14)

D) 3√(53)

10) b = √(7), c = √(12)

A) √(5)

B) 5

C) 19

D) √(19)

Solve the problem.

11) Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter.

A) 115.3 m

B) 143.2 m

C) 70 m

D) 8.4 m

12) Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 7 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 12 feet from the bottom of the pole. To the nearest tenth of a foot, find the length of the rope.

A) 193 ft.

B) 13.9 ft.

C) 4.4 ft.

D) 9.7 ft.

13) Find the length of x in the diagram below.

A) x = 7 - 1

B) x = √(105)

C) x = √(105) - 3

D) x = √(137) - 3

14) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 90 feet from where the rope is staked down. Find the altitude of the balloon if the rope is 120 feet long.

A) √(30) ft

B) 150 ft

C) 30√(7) ft

D) 3√(70) ft

15) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 30 feet from where the rope is staked down. Find the length of the rope if the altitude of the balloon is 50 feet.

A) 20√(2) ft

B) 40 ft

C) 10√(34) ft

D) 80 ft

16) A formula used to determine the velocity v in feet per second of an object (neglecting air resistance) after it has fallen a certain height is v = √(2gh), where g is the acceleration due to gravity and h is the height the object has fallen. If the acceleration g due to gravity on Earth is approximately 32 feet per second, find the velocity of a bowling ball after it has fallen 90 feet. (Round to the nearest tenth.)

A) 5760 ft per sec

B) 53.7 ft per sec

C) 13.4 ft per sec

D) 75.9 ft per sec

17) For a cone, the formula r = √((3V/πh)) describes the relationship between the radius r of the base, the volume V, and the height h. Find the volume if the radius is 6 inches and the cone is 8 inches high. (Use 3.14 as an approximation for π, and round to the nearest tenth.)

A) 50.2 cubic in.

B) 37.7 cubic in.

C) 301.4 cubic in.

D) 2713.0 cubic in.

18) Police use the formula s = √(30fd) to estimate the speed s of a car in miles per hour, where d is the distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on a certain gravel road is 0.26 and a car skidded 350 feet, find the speed of the car, to the nearest mile per hour.

A) 52 mph

B) 2730 mph

C) 286 mph

D) 102 mph

19) Police use the formula s = √(30fd) to estimate the speed s of a car in miles per hour, where d is the distance in feet that the car skidded and f is the coefficient of friction. If the coefficient of friction on a certain dry road is 0.85 and a car was traveling on it at a rate of 50 mph, how far will the car skid? (Round to the nearest foot.)

A) 83 ft.

B) 36 ft.

C) 98 ft.

D) 638 ft.

20) The formula v = √(2.5r) can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the maximum safe speed for a curve in a road with a radius of curvature of 150 feet.

A) 8 mph

B) 19 mph

C) 31 mph

D) 12 mph

21) The formula v = √(2.5r) can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the radius of curvature if the maximum safe velocity is 40.

A) 256 ft.

B) 1600 ft.

C) 640 ft.

D) 4000 ft.

22) The maximum distance d in kilometers that you can see from a height h in meters is given by the formula d = 3.5√(h). How far can you see from the top of a 428-meter building? (Round to the nearest tenth of a kilometer.)

A) 20.7 km

B) 38.7 km

C) 72.4 km

D) 800.7 km

23) The maximum distance d in kilometers that you can see from a height h in meters is given by the formula d = 3.5√(h). How high above the ground must you be to see 60 kilometers. (Round to the nearest tenth of a meter.)

A) 293.9 m

B) 1028.6 m

C) 17.1 m

D) 27.1 m

 

Solution
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