Exercise 17 Page 523

We want to find the area of △ QRS. To do so, we will use the formula for finding the area of a triangle using sine. This formula says that the area of a triangle is equal to one-half the product of the lengths of two sides of the triangle times the sine of their included angle.
Area=1/2qs sin R Since we are given that q= 9, s= 5, and m∠ R= 57^(∘), we can substitute these values into the formula to find the area. Let's do it!

Area=1/2qs sin R

SubstituteValues

Substitute values

Area=1/2( 9)( 5) sin 57^(∘)

▼

Simplify right-hand side

Multiply

Multiply

Area=1/2(45) sin 57^(∘)

MoveRightFacToNumOne

1/b* a = a/b

Area=45/2 sin 57^(∘)

CalcQuot

Calculate quotient

Area=22.5 sin 57^(∘)

UseCalc

Use a calculator

Area=18.87008...

RoundDec

Round to 1 decimal place(s)

Area ≈ 18.9

The area of △ QRS is about 18.9 square units.