Exercise 20 Page 675

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 value of x. Consider the given triangle.

We know the measures of two angles and also know the length of a side. To use the Law of Sines, we need to have the angles and corresponding sides which are opposite to these angles. Therefore, let's first find the third interior angle of the given triangle by using Triangle Angle Sum Theorem. 180 - ( 39^(∘) + 118^(∘)) = 23^(∘) We know that the length of a side is 12 units and that the measure of its opposite angle is 23^(∘). We want to find the length of the side that is opposite to the angle whose measure is 39^(∘). Now, we can use the Law of Sines! sin 23/12=sin 39/x Let's solve the above equation for x using the Cross Product Property.

sin 23/12=sin 39/x

▼

Solve for x

CrossMult

Cross multiply

x * sin 23 = 12 * sin 39

DivEqn

.LHS /sin 23.=.RHS /sin 23.

x= 12 * sin 39/sin 23

UseCalc

Use a calculator

x = 19.327471...

RoundDec

Round to 1 decimal place(s)

x≈ 19.3