Exercise 36 Page 705

Start by finding the measure of ∠ B using the Triangle Angle Sum Theorem. Then use the Law of Sines.

14.9

Practice makes perfect

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/cWe will use this law to find the value of x. Let's consider the given triangle.

Notice that, with the given information the Law of Sines will not be useful yet. First, we need to find the measure of ∠ B. To do so, we need to recall the Triangle Angle Sum Theorem. It tells us that the measures of angles in a triangle add to 180. m∠ A + m∠ B + m∠ C = 180 We are given that m∠ A = 33 and m∠ C= 86. Let's substitute these values into the above equation and solve for m∠ B.

m∠ A + m∠ B + m∠ C = 180

SubstituteII

m∠ A= 33, m∠ C= 86

33+ m∠ B + 86=180

AddTerms

Add terms

m∠ B + 119=180

SubEqn

LHS-119=RHS-119

m∠ B = 61

We found that the measure of ∠ B is 61^(∘). Let's add this information to our diagram.

Now, we know that the length of a side is 24 and that the measure of its opposite angle is 61. We want to find the length of the side that is opposite to the angle whose measure is 33. We can use the Law of Sines to do that. sin 61^(∘)/24=sin 33^(∘)/x Let's solve the above equation for x using the Cross Product Property.

sin 61^(∘)/24=sin 33^(∘)/x

CrossMult

Cross multiply

sin 61^(∘)* x=sin 33^(∘)* 24

DivEqn

.LHS /sin 61^(∘).=.RHS /sin 61^(∘).

x=sin 33^(∘)* 24/sin 61^(∘)

UseCalc

Use a calculator

x=14.94516...

RoundDec

Round to 1 decimal place(s)