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Home , Hypotenuse

legs hypotenuse

3 9 4 16

25 5 https://www.youtube.com/watch?v=uaj0XcLtN5c https://www.youtube.com/watch?v=CAkMUdeB06o

Pythagorean Theorm This theory states that the sum of the squares of the two legs of a right trangle is equal to the square of the hypotenuse.

hypotenuse (leg)2 + (leg)2 = (hypotenuse)2 leg c 2 2 2 a a + b = c

OR (hypotenuse)2 =(leg)2 + (leg)2 c2 = a2 + b2 b leg Find the length of the hypotenuse of this . Round your answer to the nearest tenth.

12 cm

16 cm ___ cm

9 cm

15 cm ___ cm 3 cm answer to the nearest tenth. to the nearest answer your Round of the . leg of the missing the length Find ___ cm ___ 12 cm 12

5 cm ___ cm ___ 13 cm 13 10 cm answer to the nearest tenth. to the nearest answer your Round of this triangle. leg of the missing the length Find ___ cm ___ 26 cm 26 15 cm 15 9 9 cm ___ cm ___ Use the to decide if the triangle below is a .

12 cm

16 cm 20 cm

7 cm

6 cm 9 cm The measures of three sides of a triangle are given. Determine whether each triangle is a right triangle. (Hint: Use the Pythagorean Theorem)

a) 5 in, 13 in, 12 in

b) 20 ft, 11 ft, 16 ft Homework Find the length of the missing side of the right triangle. If necessary, round to the nearest tenth.

2 2 2 12 + 16 = c 102 + b2 = 142

c= 20 ft c= 9.8 cm

a2 + 42 = 202 7.22 + 2.72 = c2

c= 19.6 ft c= 7.7 cm 5) The measures of three sides of a triangle are given. Determine whether each triangle is a right triangle. (Hint: Use the Pythagorean Theorem)

a) 9m, 12m, 15m

b) 6in, 7in, 12in 12 yards

16 yards

The goalie is 4 feet tall

The kicker will kick the ball 20 feet and hit the goalie on the head

How many feet away is the kicker from the goalie? Applying The Pythagorean Theorem: (Round all answers to the nearest tenth if necessary.)

1) If the lengths of the legs of a right triangle are 3 inches and 4 inches. What is the length of the hypotenuse?

2) You're locked out of your house and the only open window is on the second floor, 25 feet above the ground. You need to borrow a ladder from one of your neighbors. There's a bush along the edge of the house, so you'll have to place the ladder 10 feet from the house. What length of ladder do you need to reach the window?

3) The length of the hypotenuse of right triangle is 13 centimeters and the length of one leg is 12 centimeters. What is the number of centimeters in the length of the other leg? 4) The base of an 8-foot ladder is placed 2 feet away from a wall. How high up the wall will the ladder reach?

5) John leaves school to go home. He walks 6 blocks north and then 8 blocks west. How far is John from school? 6) A 35 foot ladder is leaning against the side of a building. The base of the ladder is 21 feet from the base of the building. How far above the ground is the where the ladder touches the building?

7) Find the length of the diagonal of a square garden whose side is 20 feet long.

8) If the length of the hypotenuse of a right triangle is 3 cm and the length of one leg is 2 cm, what is the length of the other leg? Homework

1) A wire reaches from the top of a 27 foot telephone pole to a point of the ground 11 feet away from the base of the pole. What is the length of the wire?

x

27ft

11ft

2) In triangle ABC, AC = 30, CB = 7, and m∠ C = 90°. Find the length of AB.

A

x 30

B C 7 3) Mr. Andrews wants to get to a satellite dish that is on the roof of his house, which is 42 feet above the ground. If the length of the ladder is 50 feet, how far must the base of the ladder be from the base of the house?

a2 + b2 = c2 42 ft 50ft (42)2 + (x)2 = (50)2 1764 + x2 = 2500 -1764 -1764 2 x x = 736 x = 27.12... 27.1 ft

4) A 6 foot tall tree casts an 11 foot shadow on the ground. How far is it from the end of the shadow to the top of the tree? a2 + b2 = c2 (6)2 + (11)2 = (x)2 2 x 36 + 121 = x 6ft 157 = x2 13.67... = x 13.7 ft 11ft