Exercise 34 Page 635

Let's begin with recalling the Pythagorean Theorem. In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Now, let's look at the given picture which presents the alternate and normal routes, which form a right triangle. Let x be the length of the missing side.

We can use the Pythagorean Theorem to evaluate the value of x. Notice that, since x represents the side length, we will consider only the positive case when taking a square root of x^2.

0.45^2+ x^2=( 3/4)^2

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Solve for x

WriteDec

Write as a decimal

0.45^2+x^2=0.75^2

CalcPow

Calculate power

0.2025+x^2=0.5625

SubEqn

LHS-0.2025=RHS-0.2025

x^2=0.36

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(0.36)

SqrtPowToNumber

sqrt(a^2)=a

x=sqrt(0.36)

CalcRoot

Calculate root

x=0.6

The length of the missing side is 0.6 miles. With this, we can evaluate the length of the alternate route. The alternate route: 0.45+ 0.6=1.05 Since we are asked to determine how much farther he will jog on his alternate route than he would have if he had followed his normal route, we should subtract the length of the normal route from the alternate route. The alternate route-The normal route 1.05- 0.75=0.3 He will jog 0.3 miles farther on his alternate route.