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
We 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.
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.
