Exercise 5 Page 634

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.

a^2+ b^2= c^2 Now, let's look at the given picture which presents the mainsail of a boat. We will assume that ∠ NML is a right angle.

Since △ NML is a right triangle, we can use the Pythagorean Theorem to evaluate the value of x.

45^2+ 60^2= x^2

CalcPow

Calculate power

2025+3600=x^2

AddTerms

Add terms

5625=x^2

RearrangeEqn

Rearrange equation

x^2=5625

Next we will take a square root of both sides of the equation. Notice that, since x represents the side length, we will consider only positive case when taking a square root of x^2.

x^2=5625

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(5625)

SqrtPowToNumber

sqrt(a^2)=a

x=sqrt(5625)

CalcRoot

Calculate root

x=75

The length of LN is 75 feet. This corresponds with answer D.