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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Special Right Triangles

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Exercise 68 Page 648

Use the Pythagorean Theorem.

2.6

Practice makes perfect

To find the missing side 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=3sqrt(2), b=x, and c=5.

Let's substitute these values into the formula and solve for x.

a^2+b^2=c^2

SubstituteValues

Substitute values

( 3sqrt(2))^2+ x^2= 5^2

▼

Solve for x

(a b)^m=a^m b^m

3^2(sqrt(2))^2+x^2=5^2

( sqrt(a) )^2 = a

3^2(2)+x^2=5^2

Calculate power

9(2)+x^2=25

Multiply

18+x^2=25

LHS-18=RHS-18

x^2=7

sqrt(LHS)=sqrt(RHS)

x=sqrt(7)

Use a calculator

x=2.64575...

Round to 1 decimal place(s)

x≈ 2.6

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

Subchapter links

Exercises p.644-648