Exercise 20 Page 536

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

To find the measure of angle ∠ D, we will start by drawing a diagram to illustrate the situation.

We know that the lengths of sides d, e, and f are 25in., 18in., and 20in., respectively. With this information and using the Law of Cosines, we can write an equation to find the measure of ∠ D.

25^2= 18^2+ 20^2-2( 18)( 20)cos D

▼

Solve for cos D

CalcPow

Calculate power

625=324+400-2(18)(20)(cos D)

Multiply

Multiply

625=324+400-720(cos D)

AddTerms

Add terms

625=724-720(cos D)

SubEqn

LHS-724=RHS-724

- 99=- 720(cos D)

DivEqn

.LHS /(- 720).=.RHS /(- 720).

- 99/- 720=cos D

CalcQuot

Calculate quotient

0.1375=cos D

To find m∠ D, we will use the inverse operation of cos, which is cos ^(- 1). 0.1375=cos D ⇔ cos ^(- 1)0.1375=m∠ D Finally, we will use a calculator.

cos ^(- 1)0.1375=m∠ D

RearrangeEqn

Rearrange equation

m∠ D=cos ^(- 1)0.1375

UseCalc

Use a calculator

m∠ D=82.09679...

RoundDec

Round to 1 decimal place(s)

m∠ D≈ 82.1

We found that m∠ D = 82.1.