PYTHAGOREAN THEOREM WORD PROBLEMS

OBJECTIVE: Students will solve for missing values using the

Pythagorean theorem for word problems

RECALL THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM STATES THAT FOR ANY RIGHT TRIANGLE:

a2 + b2 = c2

WORD PROBLEMS!! Most Pythagorean Theorem Questions are given as word

problems.

STEPS FOR SOLVING PYTHAGOREAN THEOREM WORD PROBLEMS:

Step 1: Circle any important numbers in the problem

Step 2: Draw a picture of the situation.

Step 3: Solve using the Pythagorean theorem (a2 + b2 = c2)

EXAMPLE 1!! 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? Step 1: Circle Important numbers.Step 2: Draw a picture of the situation.

25 fe

et

10 feet

EXAMPLE 1!! 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?

25 fe

et

10 feet

STEP 3: PYTHAGOREAN THEOREMa2 + b2 = c2

102 + 252 = c2

100 + 625 = c2

725 = c2

C = 26.92 feet

EXAMPLE 2!!

Mr. Young is measuring his TV. The TV is 36 inches wide and 24 inches tall. What is the length of the diagonal on the TV?

Step 1: Circle Important numbers.Step 2: Draw a picture of the situation.

36 inches

24 in

ches

STEP 3: PYTHAGOREAN THEOREMa2 + b2 = c2

362 + 242 = c2

1296 + 576 = c2

1872 = c2

C = 43.26 inches

EXAMPLE 3!!Firefighters have a 40 foot extension ladder. In order

to reach 28 feet up a building, how far away from the building should the foot of the ladder be placed?Step 1: Circle Important numbers.

Step 2: Draw a picture of the situation.STEP 3: PYTHAGOREAN THEOREM

a2 + b2 = c2

40 fe

et

28 fe

et

b

282 + b2 = 402

784 + b2 = 1600b2 = 816

b = 28.57 feet