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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

7. Law of Sines and Law of Cosines

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Exercise 9 Page 513

Use the formula for finding the area of a triangle using sine, 12bc sin A.

≈ 81.8 square units

Practice makes perfect

We want to find the area of △ ABC.

To do so, we will use the formula for finding the area of a triangle using sine. Area=1/2bc sin A Since we are given that b= 15, c= 13, and m∠ A= 57^(∘), we can substitute these values into the formula to find the area. Let's do it!

Area=1/2bc sin A

SubstituteValues

Substitute values

Area=1/2( 15)( 13) sin 57^(∘)

▼

Simplify right-hand side

Multiply

Area=1/2(195) sin 57^(∘)

MoveRightFacToNumOne

1/b* a = a/b

Area=195/2 sin 57^(∘)

Calculate quotient

Area=97.5 sin 57^(∘)

Use a calculator

Area=97.5(0.838670... )

Multiply

Area=81.770325...

Round to 1 decimal place(s)

Area≈ 81.8

The area of △ ABC is about 81.8 square units.

Subchapter links

Communicate Your Answer p.507

Monitoring Progress p.508-512

Exercises p.513-516