Exercise 60 Page 690

For any △ ABC, let the lengths of the sides opposite angles A, B, and C be a, b, and c, respectively.

sin A/a=sin B/b=sin C/c Let's use this law to find the values of x. Consider the given triangle.

We know that the length of a side is 41 and that the measure of its opposite angle is 19^(∘). We want to find the length of the side that is opposite to the angle whose measure is 111^(∘). With this information and using the Law of Sines, we can write an equation in terms of x. sin 19^(∘)/41=sin 111^(∘)/x Let's solve the above equation for x using the Cross Product Property.

sin 19^(∘)/41=sin 111^(∘)/x

CrossMult

Cross multiply

sin 19^(∘)* x=41* sin 111^(∘)

DivEqn

.LHS /sin 19^(∘).=.RHS /sin 19^(∘).

x=41* sin 111^(∘)/sin 19^(∘)

UseCalc

Use a calculator

x=117.56923...

RoundDec

Round to 1 decimal place(s)

x≈ 117.6