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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Trigonometry

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Exercise 69 Page 659

Notice that the area of a right triangle is half of the product of the lengths of its legs.

E

Practice makes perfect

We are given that the area of a right triangle is 240 square inches and the base is 30 inches long. Let x and y represent the missing sides.

Let's recall that in a right triangle the area is half of the product of the lengths of its legs. 240=1/2* 30* xWe can solve the above equation for x.

240=1/2*30* x

▼

Solve for x

MoveRightFacToNum

a/c* b = a* b/c

240=30/2* x

Calculate quotient

240=15* x

.LHS /15.=.RHS /15.

16=x

Rearrange equation

x=16

The second leg has a length of 16 inches long. Let x and y represent the missing sides.

Next we can evaluate the length of the hypotenuse y using the Pythagorean Theorem. Recall that, according to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse. 30^2+ 16^2= y^2 Let's solve the equation. Notice that, since y represents the side length, we will consider only the positive case when taking a square root of y^2.

30^2+16^2=y^2

▼

Solve for y

Calculate power

900+256=y^2

Add terms

1156=y^2

Rearrange equation

y^2=1156

sqrt(LHS)=sqrt(RHS)

sqrt(y^2)=sqrt(1156)

SqrtPowToNumber

sqrt(a^2)=a

y=sqrt(1156)

Calculate root

y=34

The length of the hypotenuse of this triangle is 34. This corresponds with answer E.

Subchapter links

Exercises p.655-659