The Pythagorean Theorem

Name Pythagorean Theorem

Alg 1 Mr. McCormack The Pythagorean Theorem:

2 2 2 For all right triangles: a + b = c (where c is the hypotenuse)

a= 3 b= 4 c= ? Pythagorean Triples c 3,4,5 3 32 + 42 = c2 5,12,13 9 + 16 = c2 7,24,25 25 = c2 8,15,17 4 25 =  c2 9, 40, 41 5 = c

Right Triangle Trigonometry: SOH-CAH-TOA SOH: sin = opposite CAH: cos = adjacent TOA: tan = opposite hypotenuse hypotenuse adjacent

hypotenuse hypotenuse adjacent opposite

A C A C opposite adjacent

Based on angle B Based on angle C

The hypotenuse is always the side opposite the right angle. The opposite and adjacent depend on which angle you are looking at. opposite: The side directly across from the angle (does not touch the angle). adjacent: (Next to) The side that touches the angle, but is not the hypotenuse.

1 Name Pythagorean Theorem

Alg 1 Mr. McCormack Find the missing side to the nearest tenth: 1) 2)

Find missing side to the nearest hundredth: 3) 4)

Find the missing side in simplest radical form: 5) 6)

7) A 30-foot ladder is leaning against a building. The base of the ladder is 16 feet away from the base of the building. How far up the building is the top of the ladder resting to the nearest tenth?

8) A pigeon leaves its nest and flies 5 km due east. The pigeon then flies 3 km due north. How far from its nest is the pigeon to the nearest hundredth?

9) The dimensions of a rectangle are 8m and 5m. Find the length of the diagonal in simplest radical form.

10) A 35-foot ladder leans against a building 20 feet above the ground. How many feet to the nearest hundredth is the base of the ladder away from the base of the building?

2 Name Pythagorean Theorem

Alg 1 Mr. McCormack 1) tenth 2) simplest radical form 3) hundredth

4) A 25-foot ladder is leaning against a building. The base of the ladder is 7 feet away from the base of the building. How far up the building is the top of the ladder resting?

5) A bird is perched in a tree. It is 35 feet off the ground. It sees a piece of bread on the ground 15 feet from the base of the tree. How far will the bird have to fly to get the bread (round to the nearest hundredth)?

6) The dimensions of a rectangle are 12m and 4m. Find the length of the diagonal in simplest radical form.

7) The area of a rectangle is 72 ft2. The length is represented by x + 1. The width is represented by x – 5. Find the length of the rectangle’s diagonal to the nearest tenth of a foot.