Warmup

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Designed by Skip Tyler, Varina High School

5

3123.25 10

32 + 2 2 + 3

What is a right triangle?

It is a triangle which has an angle that is 90 degrees.

The two sides that make up the right angle are called legs.

The side opposite the right angle is the hypotenuse.

leg

leg

hypotenuse

right angle

The Pythagorean Theorem

In a right triangle, if a and b are the measures of the legs and c is the

hypotenuse, then

a2 + b2 = c2.

Note: The hypotenuse, c, is always the longest side.

Find the length of the hypotenuse,

if a = 3 and b = 432 + 42 = c2

9 + 16 = c2

25 = c2

Take the square root of both sides.

5 = c

225 c

52 + 122 = c2

25 + 144 = c2

169 = c2

Take the square root of both sides.

13 = c

Find the length of the hypotenuse, if a = 5 and b = 12.

2169 c

Find the length of the hypotenuse given a = 9 and b = 12

1. 21

2. 225

3. 15

4. 18

Find the length of the leg, if a = 7 and c = 25.

72 + b2 = 252

49 + b2 = 625Solve for b.

16 - 49 + b2 = 625 - 49b2 = 576

b = 24

2 576b

Find the length of the missing side given a = 4 and c = 5

1. 1

2. 3

3. 6.4

4. 9

• A 30-m garden hose is stretched diagonally across a yard. If the width of the yard is 18-m, what is the length of the yard?

30 m.

?182 + b2 = 302 324 + b2 = 900324 – 324 + b2 = 900 – 324b2 = 576b = 24

• A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 50 feet long. The water is 48 feet deep. How far is the anchor from a point directly below the boat?

50 feet

48 feet