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Word Problem We actually see the Pythagorean Theorem used in our daily lives. For example a television is measured by the diagonal dimension of its screen. For example, a 24-in television has a diagonal measure of 24 in.
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PYTHAGOREANWORD PROBLEMS
Word Problems Today’s focus is going to be on the
dreaded word problems. More often problems that need to be solved using the Pythagorean Theorem appear as word problems. This is where everything we have been doing in this unit comes together.
Word Problem We actually see the
Pythagorean Theorem used in our daily lives. For example a television is measured by the diagonal dimension of its screen. For example, a 24-in television has a diagonal measure of 24 in.
Word Problems The first thing you always want to do
when solving a word problem, is draw a picture. The pictures aids in making sure that you label the correct sides.
Word Problems – Example 1 A television screen is 16 in high and 22
in wide. What is its diagonal dimension to the nearest whole number?
Word Problems – Example 1 A television screen is 16 in high and 22
in wide. What is its diagonal dimension to the nearest whole number? Remember to first draw a picture
Word Problems – Example 1 A television screen is 16 in high and 22
in wide. What is its diagonal dimension to the nearest whole number? Remember to first draw a picture
16 in
Word Problems – Example 1 A television screen is 16 in high and 22
in wide. What is its diagonal dimension to the nearest whole number? Remember to first draw a picture
16 in
22 in
Word Problems – Example 1 A television
screen is 16 in high and 22 in wide. What is its diagonal dimension to the nearest whole number? Remember to first
draw a picture
a2 + b2 = c2
16 in
22 in
Word Problems – Example 1 A television
screen is 16 in high and 22 in wide. What is its diagonal dimension to the nearest whole number? Remember to first
draw a picture
a2 + b2 = c2
162 + 222 = c2
16 in
22 in
Word Problems – Example 1 A television
screen is 16 in high and 22 in wide. What is its diagonal dimension to the nearest whole number? Remember to first
draw a picture
a2 + b2 = c2
162 + 222 = c2
256 + 484 = c2
740 = c2
27.2 = c Therefore the
television has a diagonal measurement of 27.2 inches.
16 in
22 in
Word Problems – Example 2 Two hikers start a trip from a camp
walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp? Remember to first draw a picture
Word Problems – Example 2 Two hikers start a trip from a camp
walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp? Remember to first draw a picture
1.5 km
Word Problems – Example 2 Two hikers start a trip from a camp
walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp? Remember to first draw a picture
1.5 km
1.7 km
Word Problems – Example 2 Two hikers start a trip
from a camp walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp?
a2 + b2 = c2
1.7 km
1.5 km
Word Problems – Example 2 Two hikers start a trip
from a camp walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp?
a2 + b2 = c2
1.72 + 1.52 = c2
1.7 km
1.5 km
Word Problems – Example 2 Two hikers start a trip
from a camp walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp?
a2 + b2 = c2
1.72 + 1.52 = c2
2.89 + 2.25 = c2
1.7 km
1.5 km
Word Problems – Example 2 Two hikers start a trip
from a camp walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp?
a2 + b2 = c2
1.72 + 1.52 = c2
2.89 + 2.25 = c2
5.14 = c2
1.7 km
1.5 km
Word Problems – Example 2 Two hikers start a trip
from a camp walking 1.5 km due east. They turn due north and walk 1.7 km to a waterfall. To the nearest tenth of kilometer, how far is the waterfall from the camp?
a2 + b2 = c2
1.72 + 1.52 = c2
2.89 + 2.25 = c2
5.14 = c2
2.3 = c Therefore the
waterfall is 2.3 km from camp.
1.7 km
1.5 km
Word Problems – Example 3 A carpenter is attaching a brace to the
back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace? Remember to first draw a picture
Word Problems – Example 3 A carpenter is attaching a brace to the
back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace? Remember to first draw a picture
40 in
30 in
Word Problems – Example 3 A carpenter is
attaching a brace to the back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace?
a2 + b2 = c2
30 in
40 in
Word Problems – Example 3 A carpenter is
attaching a brace to the back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace?
a2 + b2 = c2
302 + 402 = c2
30 in
40 in
Word Problems – Example 3 A carpenter is
attaching a brace to the back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace?
a2 + b2 = c2
302 + 402 = c2
900 + 1600 = c2
30 in
40 in
Word Problems – Example 3 A carpenter is
attaching a brace to the back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace?
a2 + b2 = c2
302 + 402 = c2
900 + 1600 = c2
2500 = c2
30 in
40 in
Word Problems – Example 3 A carpenter is
attaching a brace to the back of a frame that measures 30 in. by 40 in. What the is length, in inches, of the brace?
a2 + b2 = c2
302 + 402 = c2
900 + 1600 = c2
2500 = c2
50 = c Therefore the
brace is 50 inches long.
30 in
40 in
Word Problems – Example 4 A diver swims 20 m under water to the
anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter. Remember to first draw a picture
Word Problems – Example 4 A diver swims 20 m under water to the
anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter. Remember to first draw a picture
20 m
Word Problems – Example 4 A diver swims 20 m under water to the
anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter. Remember to first draw a picture
20 m10 m
Word Problems – Example 4 A diver swims 20 m
under water to the anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter.
a2 + b2 = c2
20 m10 m
Word Problems – Example 4 A diver swims 20 m
under water to the anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter.
a2 + b2 = c2
102 + b2 = 202
20 m10 m
Word Problems – Example 4 A diver swims 20 m
under water to the anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter.
a2 + b2 = c2
102 + b2 = 202
100 + b2 = 400
20 m10 m
Word Problems – Example 4 A diver swims 20 m
under water to the anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter.
a2 + b2 = c2
102 + b2 = 202
100 + b2 = 400 b2 = 400 – 100
20 m10 m
Word Problems – Example 4 A diver swims 20 m
under water to the anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter.
a2 + b2 = c2
102 + b2 = 202
100 + b2 = 400 b2 = 400 – 100 b2 = 300
20 m10 m
Word Problems – Example 4 A diver swims 20 m
under water to the anchor of a buoy that is 10 m below the surface of the water. On the surface, how far is the buoy located from the place where the diver started? Round to the nearest meter.
a2 + b2 = c2
102 + b2 = 202
100 + b2 = 400 b2 = 400 – 100 b2 = 300 b = 17.3 m Therefore the buoy
is 17.3 meters from where the diver started.
20 m10 m
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