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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Standardized Test Practice

Exercise 7 Page 711

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

93.9

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 value 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 to write an equation in terms of x.

25^2= 15^2+ 19^2-2( 15)( 19)cos x^(∘)

▼

Solve for cos x^(∘)

Calculate power

625=225+361-2(15)(19)cos x^(∘)

Add terms

625=586-2(15)(19)cos x^(∘)

Multiply

625=586-570cos x^(∘)

LHS-586=RHS-586

39=- 570cos x^(∘)

.LHS /(- 570).=.RHS /(- 570).

39/- 570=cos x^(∘)

MoveNegDenomToFrac

Put minus sign in front of fraction

-39/570=cos x^(∘)

Rearrange equation

cos x^(∘)=-39/570

To find the value of x we will use the inverse operation of cos, which is cos ^(- 1). cos x^(∘)=-39/570 ⇕ x=cos ^(- 1)(-39/570) Finally, we will use a calculator.

x=cos ^(- 1)(-39/570)

Use a calculator

x=93.92330...

Round to 1 decimal place(s)

x≈ 93.9

Subchapter links

Multiple Choice p.710

Short Response/Gridded Response p.711

Extended Response p.711