PYTHAGOREAN THEOREM WORD PROBLEMS. OBJECTIVE: Students will solve for missing values using the Pythagorean theorem for word problems

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1 PYTHAGOREAN THEOREM WORD PROBLEMS OBJECTIVE: Students will solve for missing values using the Pythagorean theorem for word problems

2 RECALL THE PYTHAGOREAN THEOREM THE PYTHAGOREAN THEOREM STATES THAT FOR ANY RIGHT TRIANGLE: a 2 + b 2 = c 2

3 Warm Up Solve for the missing side in each right triangle below. Remember: a 2 + b 2 = c 2 1.) 2.) 3 c b 7 4 2

4 Warm Up ANSWERS Solve for the missing side in each right triangle below. Remember: a 2 + b 2 = c c 2. b = c 2 25 = c 2 c = 5 2 b = 7 2 b = 49 b 2 = 45 b = 45 = 6.7

5 WORD PROBLEMS Many 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 (a 2 + b 2 = c 2 )

6 EXAMPLE 1 Mr. Blonde is measuring his TV. The TV is 12 inches wide and 9 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. STEP 3: PYTHAGOREAN THEOREM a 2 + b 2 = c = c = c = c 2 C = 225 = 15 in 12 inches 9 inches

7 EXAMPLE 2 Mr. Blue is measuring his TV. The TV is 12 inches wide and 5 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. STEP 3: PYTHAGOREAN THEOREM a 2 + b 2 = c = c = c = c 2 C = 169 = 13 in 12 inches 5 inches

8 EXAMPLE 3 Tim & Sal have a 10 meter ladder. It must reach exactly 6 meters up a building, how far away from the building should the ladder be placed? Step 1: Circle Important numbers. Step 2: Draw a picture of the situation. STEP 3: PYTHAGOREAN THEOREM a 2 + b 2 = c b 2 = b 2 = 100 b 2 = 64 b = 64 = 8 feet b 6 Meters

9 EXAMPLE 4 Eric & Emily have a 5 meter ladder. It must reach exactly 3 meters up a building, how far away from the building should the ladder be placed? Step 1: Circle Important numbers. Step 2: Draw a picture of the situation. STEP 3: PYTHAGOREAN THEOREM a 2 + b 2 = c b 2 = b 2 = 25 b 2 = 16 b = 16 = 4 meters b 3 Meters

10 Example 5 Tim rode 3 miles due north, then 3 miles due east. How far, to the nearest mile, is Tim from where he started? Draw a diagram: 3 3 x

11 Ex = x = x 2 18 = x 2 x = 18 = 4.2 Tim is 4.2 miles from where he started.

12 Example 6 Mary rode 4 miles due north, then 4 miles due east. How far, to the nearest mile, is Mary from where he started? Draw a diagram: 4 4 x

13 Ex = x = x 2 32 = x 2 x = 32 = 5.6 Mary is 5.6 miles from where he started.

14 Example 7 Town X is 30 miles directly west town Y. Town Z is 40 miles south of town Y. Tom lives in X and wants to get to Z. How much shorter is the direct route from town X to town Z than the longer route traveling through town Y? X 30 miles Y a 2 + b 2 = c =c = c 2??? 40 miles 2500 = c² 50 = c Z Did I answer question?

15 Ex 7 Long route = 70 miles Short route = 50 miles = miles shorter.

16 Example 8 A boat sails due East from a Harbour (H), to a marker buoy (B),3 miles away. AtB the boat turns due South and sails for 2. miles to a Lighthouse (L). It then returns straight to harbour. What is the total distance travelled by the boat? H 3 miles B = c = c 2 13 = c 2 C 2 = 13 = 3.6 Total distance travelled = = 8.6 miles L 2 miles

17 ex 9 The length of a rectangle is 8 in, the length of its diagonal is 10 in. Find the area of the rectangle. Area of rectangle A = L x W We need the width! 10 in b a 2 + b 2 = c b 2 = b 2 = 100 b 2 = b 2 = 36 b = 36 = 6 8 in area = 8 x 6 area = 48 sq inches

18 Use your calculator for the rest

19 EXAMPLE 10 You're locked out of your house and the only open window is on the second floor, 24 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 7 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. 7 feet 24 feet

20 EXAMPLE 10 You're locked out of your house and the only open window is on the second floor, 24 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 7 feet from the house. What length of ladder do you need to reach the window? STEP 3: PYTHAGOREAN THEOREM a 2 + b 2 = c = c = c = c 2 C = 625 = 25 feet 7 feet 24 feet

21 Ex 11 On a regulation baseball field, the bases are 90 ft apart. How far is it on a direct line from 1 st base to 3 rd base? 3 rd base 1 st base a 2 + b 2 = c = c = c = c 2 C2 = = ft home plate

22 EXAMPLE 12 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 a 2 + b 2 = c b 2 = b 2 = 1600 b 2 = 816 b = 816 = 28.6 feet b 28 feet

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