Exercise 121 Page 368

Consider the Law of Sines and the Law of Cosines.

x≈ 17.06

We are asked to solve for x twice. The first method we can use is the Law of Sines.

sin A/a=sin B/b

SubstituteValues

Substitute values

sin 81^(∘)/28=sin 37^(∘)/x

MultEqn

LHS * x=RHS* x

sin 81^(∘)/28* x=sin 37^(∘)

MultEqn

LHS * 28=RHS* 28

sin 81^(∘)* x=28sin 37^(∘)

DivEqn

.LHS /sin 81^(∘).=.RHS /sin 81^(∘).

x=28sin 37^(∘)/sin 81^(∘)

UseCalc

Use a calculator

x=17.06086...

RoundDec

Round to 2 decimal place(s)

x≈ 17.06

Second, we can also use the Law of Cosines to determine the value of x.

c^2=a^2+b-2abcos θ

SubstituteValues

Substitute values

x^2=25^2+28^2-2(25)(28)cos 37^(∘)

CalcPow

Calculate power

x^2=625+784-2(25)(28)cos 37^(∘)

Multiply

x^2=625+784-1118.08971...

AddSubTerms

Add and subtract terms

x^2=290.91028...

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± 17.05609...

x > 0

x= 17.05609...

RoundDec

Round to 2 decimal place(s)

x≈ 17.06

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Exercise 121 Page 368

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