Exercise 1 Page 709

We are given that Christine is flying a kite on the end of a taut string, and we know that the kite is 175 feet above the ground and that its horizontal distance is 130 feet from where Christine is standing. Let's sketch a diagram describing the given situation. Let x represent the length of the kite string.

Notice that the horizontal distance is perpendicular to the vertical distance. Therefore, we can use the Pythagorean Theorem to evaluate the value of x. Let's recall this 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.

a^2+ b^2= c^2 Using this theorem, we can create an equation to find the value of x. 175^2+ 130^2=x^2 Let's solve the equation. Notice that, since x represents a length, we will consider only the positive case when taking a square root of x^2.

175^2+130^2=x^2

CalcPow

Calculate power

30625+16900=x^2

AddTerms

Add terms

47525=x^2

RearrangeEqn

Rearrange equation

x^2=47525

▼

sqrt(LHS)=sqrt(RHS)

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(47525)

SqrtPowToNumber

sqrt(a^2)=a

x=sqrt(47525)

CalcRoot

Calculate root

x=218.0022...

RoundInt

Round to nearest integer

x≈ 218

The length of the kite string Christine let out is approximately 218 feet. This corresponds with option B.