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 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 the Triangle Angle Sum Theorem.
180 - ( 105^(∘) + 18^(∘)) = 57^(∘)
We know that the length of a side is 22 units and that the measure of its opposite angle is 57^(∘). We want to find the length of the side that is opposite to the angle whose measure is 18^(∘). Now, we can use the Law of Sines!
sin 18/x=sin 57/22
Let's solve the above equation for x using the Cross Product Property.
