Exercise 59 Page 690

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

The Law of Sines relates the sine of each angle to the length of the opposite side. 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 53 and that the measure of its opposite angle is 48^(∘). We also know that the length of the side that is opposite to the angle we want to find is 68. With this information and using the Law of Sines, we can write an equation in terms of x. sin x^(∘)/68=sin 48^(∘)/53 Let's solve our equation!

sin x^(∘)/68=sin 48^(∘)/53

MultEqn

LHS * 68=RHS* 68

sin x^(∘)=sin 48^(∘)/53* 68

To find x we will use the inverse operation of sin, which is sin ^(- 1). sin x^(∘)=sin 48^(∘)/53* 68 ⇕ x=sin ^(- 1)(sin 48^(∘)/53* 68) Finally, we will use a calculator.

x=sin ^(- 1)(sin 48^(∘)/53* 68)

UseCalc

Use a calculator

x=72.45278...

RoundInt

Round to nearest integer

x≈ 72