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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. The Law of Sines and Law of Cosines

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Exercise 27 Page 675

The Law of Cosines relates the cosine of each angle in a triangle to its side lengths.

112

Practice makes perfect

For any △ ABC, the Law of Cosines relates the cosine of each angle to the side lengths of the triangle.

Let's use this law to find the values of x. Consider the given triangle.

We know the three side lengths and want to find one of the interior angles of the triangle. We can use the Law of Cosines!

( 6.5)^2=( 5.6)^2+( 1.8)^2-2( 5.6)( 1.8)cos x^(∘)

▼

Solve for cos x^(∘)

Calculate power

42.25=31.36+3.24-2(5.6)(1.8)cos x^(∘)

Add terms

42.25=34.6-2(5.6)(1.8)cos x^(∘)

Multiply

42.25=34.6-20.16cos x^(∘)

LHS-34.6=RHS-34.6

7.65=- 20.16cos x^(∘)

.LHS /(- 20.16).=.RHS /(- 20.16).

7.65/- 20.16=cos x^(∘)

Use a calculator

- 0.379464...=cos x^(∘)

Rearrange equation

cos x^(∘)=- 0.379464...

To find the value of x we will use the inverse operation of cos, which is cos ^(- 1). cos x^(∘)=- 0.379464... ⇕ x=cos ^(- 1)(- 0.379464...) Finally, we will use a calculator.

x=cos ^(- 1)(- 0.379464...)

Use a calculator

x=112.300485...

Round to nearest integer

x≈ 112

Subchapter links

Exercises p.674-679