Transcript PYTHAGOREAN THEOREM WORD PROBLEMS

DO NOW!!!
 Solve for the missing side in each right
triangle below.
 Remember: a2 + b2 = c2
2.)
1.)
c
5
40
b
12
24
DO NOW!!! ANSWERS
 Solve for the missing side in each right
triangle below.
 Remember: a2 + b2 = c2
2.
1.
c
5
40
b
12
C = 13
24
B = 32
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:
2
a
+
2
b
=
2
c
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?
25 feet
Step 1: Circle Important numbers.
Step 2: Draw a picture of the situation.
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 feet
STEP 3: PYTHAGOREAN THEOREM
a2 + b2 = c2
102 + 252 = c2
100 + 625 = c2
725 = c2
C = 26.92 feet
10 feet
EXAMPLE 2!!
Step 1: Circle Important numbers.
Step 2: Draw a picture of the situation.
STEP 3: PYTHAGOREAN THEOREM
a2 + b2 = c2
362 + 242 = c2
1296 + 576 = c2
1872 = c2
C = 43.26 inches
24 inches
 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?
36 inches
EXAMPLE 3!!
Step 1: Circle Important numbers.
Step 2: Draw a picture of the situation.
STEP 3: PYTHAGOREAN THEOREM
a2 + b2 = c2
282 + b2 = 402
784 + b2 = 1600
b2 = 816
b = 28.57 feet
28 feet
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?
b
PRACTICE PROBLEMS
 TRY THE FOLLOWING PRACTICE
PROBLEMS TO BE COLLECTED AND
GRADED AT THE END OF THE
PERIOD.
 IF YOU FINISH EARLY, TRY THE
BONUS PROBLEMS WORTH 5 bonus
POINTS EACH.