Exercise 19 Page 526

For any △ ABC, let the lengths of the sides opposite to 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 value of x. Consider the given triangle.

We know that the length of a side is 5 in. and that the measure of its opposite angle is 43^(∘). We also know that the measure of the angle that is opposite to the side we want to find is 74^(∘). With this information and using the Law of Sines, we can write an equation in terms of x. sin 43^(∘)/5=sin 74^(∘)/x Let's solve our equation!

sin 43^(∘)/5=sin 74^(∘)/x

CrossMult

Cross multiply

sin 43^(∘)* x=sin 74^(∘)* 5

DivEqn

.LHS /sin 43^(∘).=.RHS /sin 43^(∘).

x=sin 74^(∘)*5/sin 43^(∘)

UseCalc

Use a calculator

x=7.047390...

RoundDec

Round to 2 decimal place(s)

x=7.05

We conclude that x= 7.05 inches.