Section 5'8 Geometry Applications:

1
Section 5.8 Geometry Applications Pythagorean
Theorem and Square Roots
is called the Square Root Symbol and is
also known as a ____________ sign.
Radical
2
The square root of a positive number a, written ,
is the number we square to get a. If b
then b2 a For example, The square of 5 is 25,
so the square root of 25 is 5.
3
Find each of the following square roots without
using a calculator
4
Find each of the following square roots without
using a calculator
5
Find each of the following square roots without
using a calculator
6
Use a calculator to find the following square
roots. If necessary, round to the nearest
hundredth.
7
Pythagorean Theorem Right Triangle triangle
that has a 90 angle Hypotenuse longest side
of a right triangle Pythagorean Theorem the
sum of the squares of the two shorter sides
of a right triangle is equal to the square of
the longest side.
leg2 leg2 hypotenuse2 or a2 b2 c2
c hypotenuse a
leg b leg
To find the hypotenuse c
To find a leg a
8
Use your calculator to find the length of the
missing side of the following right triangles
If necessary, round your answer to the nearest
hundredth.
11.
5 yd
5 yd
c ?
c 7.07 yd
9
Use your calculator to find the length of the
missing side of the following right triangles
If necessary, round your answer to the nearest
hundredth.
12.
25 cm
7 cm
c ?
c 25.96 cm
10
Use your calculator to find the length of the
missing side of the following right triangles
If necessary, round your answer to the nearest
hundredth.
13.
9 mi
a ?
11 mi
a 6.32 mi
11
Use your calculator to find the length of the
missing side of the following right triangles
If necessary, round your answer to the nearest
hundredth.
13.
a ?
6 m
14 m
a 12.65 m
12
15. Two children are trying to cross a stream.
They want to use a log that goes from one bank
to the other. If the left bank is 5 feet higher
than the right bank and the stream is 12 feet
wide, how long must a log be to just barely
reach?
c ?
5 ft
12 ft
The log needs to be 13 ft long.
13
16. A wire from the top of a 24-foot pole is
fastened to the ground by a stake that is 10
feet from the bottom of the pole. How long is
the wire?
c ?
24 ft
10 ft
The wire is 26 feet long.
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Sec 5.8 Pythagorean Theorem and Square Roots Pg.
377 1 15 odd, 19 43 odd, 24, 30, 36, 38, 44
15
Section 5.9 Problem Solving Equations Containing
Decimals Use a calculator to help you solve
each equation and make sure to show all steps
1. x 23.2 -4.5 2. 7x 0.63
-7 -7
x 23.2 -4.5
23.2 23.2
x 0.09
x 18.7
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Use a calculator to help you solve each equation
and make sure to show all steps 3. 2x
3.8 - 7.7
2x 3.8 -7.7
3.8 3.8
2x -11.5
2 2
x 5.75
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Use a calculator to help you solve each equation
and make sure to show all steps 4. 2x
3.3 7x 5.2
2x 3.3 7x 5.2
2x 2x
-3.3 5x 5.2
-3.3 5x 5.2
5.2 5.2
1.9 5x
5 5
x 0.38
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Use a calculator to help you solve each equation
and make sure to show all steps 5. 0.7x
0.32 0.5x 0.56
0.7x 0.32 0.5x 0.56
0.5x 0.5x
0.2x 0.32 0.56
0.2x 0.32 0.56
0.32 0.32
0.2x 0.88
0.2 0.2
x 0.44
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Use a calculator to help you solve each equation
and make sure to show all steps 6. 0.1x
0.5(x 8) 7
0.1x 0.5x 7
4
0.6x 4 7
0.6x 4 7
4 4
0.6x 3
0.6 0.6
x 5
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Steps for Solving Word Problems with Two
Unknowns 1. Read the Problem. 2. Assign a
variable to the unknown you know the least about.
Let X 3. When there is more than one
unknown, write an expression using the same
variable. 4. Write an algebraic equation. 5.
Solve the equation. 6. Answer the question.
7. Check the reasonableness of your answer.
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Solve the following word problems. Make sure to
write a Let Statement, write the equation,
solve the equation, and write your answer using
complete sentences. 7. A car rental company
charges 12 a day and 18 cents per mile to rent
their cars. If the total charge for a 1-day
rental was 33.78, how many miles was the car
driven?
Let X number of miles driven
0.18x 1 12 33.78
0.18x 12 33.78
12 12
The rental car was driven 121 miles.
0.18x 21.78
0.18 0.18
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8. The cost for a long distance call is 23 cents
for the first minute and 14 cents for each
additional minute. If the total charge for the
call is 3.73, how many minutes was the call?
Let X number of minutes used
0.231 0.14x 3.73
0.23 0.14x 3.73
0.23 0.23
0.14x 3.50
The long distance call lasted 25 minutes.
0.14 0.14
23
9. A car rental company charges 11 a day and 18
cents per mile to rent their cars. If the total
charge for a 2-day rental was 61.60, how many
miles was the car driven?
Let X number of miles driven
11 2 0.18x 61.60
22 0.18x 61.60
22 22
0.18x 39.60
0.18 0.18
The car was driven 220 miles.
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Sec 5.9 Equations with decimals Pg. 381 1
25 odd, 14, 18, 20, 22, 24, 26