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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^2

In 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

a= 7, c= 30

7^2+b^2= 30^2

▼

Solve for b

Calculate power

49+b^2=900

LHS-49=RHS-49

b^2=851

sqrt(LHS)=sqrt(RHS)

sqrt(b^2)=sqrt(851)

SqrtPowToNumber

sqrt(a^2)=a

b=sqrt(851)

Calculate root

b=29.171904...

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

9.2.1 Side Lengths and Triangles p.413-415

9.2.2 Pythagorean Theorem p.420

9.2.3 Understanding Square Root p.425-427

9.2.4 Real Numbers p.432-434

9.2.5 Applications of the Pythagorean Theorem p.437

9.2.6 Pythagorean Theorem in Three Dimensions p.440-441

9.2.7 Pythagorean Theorem Proofs p.444-445