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Core Connections: Course 3
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Core Connections: Course 3 View details
2. Section 9.2
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Exercise 140 Page 440

Use the Pythagorean Theorem.

About 29.17mm

Practice makes perfect

To find the missing side length of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=7mm and c=30mm.

Triangle

Let's substitute these values into the formula.

a^2+b^2=c^2
SubstituteII

a= 7, c= 30

7^2+b^2= 30^2
â–¼
Solve for b
CalcPow

Calculate power

49+b^2=900
SubEqn

LHS-49=RHS-49

b^2=851
SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(b^2)=sqrt(851)
SqrtPowToNumber

sqrt(a^2)=a

b=sqrt(851)
CalcRoot

Calculate root

b=29.171904...
RoundDec

Round to 2 decimal place(s)

b≈ 29.17

Since a negative side length does not make sense, we only need to consider positive solutions.

Subchapter links expand_more
arrow_right 9.2.1 Side Lengths and Triangles p.413-415
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60
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62
Side Lengths and Triangles 63 (Page 415)
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67
arrow_right 9.2.2 Pythagorean Theorem p.420
74
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78
Pythagorean Theorem 79 (Page 420)
arrow_right 9.2.3 Understanding Square Root p.425-427
Understanding Square Root 88 (Page 425)
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Understanding Square Root 91 (Page 425)
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Understanding Square Root 96 (Page 426)
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Understanding Square Root 98 (Page 427)
Understanding Square Root 99 (Page 427)
arrow_right 9.2.4 Real Numbers p.432-434
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111
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Real Numbers 113 (Page 433)
Real Numbers 114 (Page 433)
Real Numbers 115 (Page 433)
Real Numbers 116 (Page 433)
Real Numbers 117 (Page 433)
Real Numbers 118 (Page 433)
Real Numbers 119 (Page 434)
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121
arrow_right 9.2.5 Applications of the Pythagorean Theorem p.437
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130
Applications of the Pythagorean Theorem 131 (Page 437)
Applications of the Pythagorean Theorem 132 (Page 437)
Applications of the Pythagorean Theorem 133 (Page 437)
Applications of the Pythagorean Theorem 134 (Page 437)
arrow_right 9.2.6 Pythagorean Theorem in Three Dimensions p.440-441
Pythagorean Theorem in Three Dimensions 139 (Page 440)
Pythagorean Theorem in Three Dimensions 140 (Page 440)
Pythagorean Theorem in Three Dimensions 141 (Page 440)
Pythagorean Theorem in Three Dimensions 142 (Page 441)
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arrow_right 9.2.7 Pythagorean Theorem Proofs p.444-445
Pythagorean Theorem Proofs 149 (Page 444)
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Pythagorean Theorem Proofs 151 (Page 444)
Pythagorean Theorem Proofs 152 (Page 444)
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Pythagorean Theorem Proofs 154 (Page 445)