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 and y. We will find them one at a time.
We know that the length of a side is 4.7cm and that the measure of its opposite angle is 51^(∘). We also know that the length of the side that is opposite to the angle we want to find is 3cm. With this information and using the Law of Sines, we can write an equation in terms of x.
sin x/3=sin 51/4.7
Let's solve our equation!
To find x we will use the inverse operation of sin, which is sin ^(- 1).
sin x=sin 51/4.7* 3
⇕
x=sin ^(- 1)(sin 51/4.7* 3)
Finally, we will use a calculator.
Knowing that x=29.7^(∘), we can find the third interior angle using the Triangle Angle Sum Theorem.
180^(∘)- 51^(∘)- 29.7^(∘)= 99.3^(∘)
Consider the triangle with the new information.
We know that the length of a side is 4.7cm and that the measure of its opposite angle is 51^(∘). We want to find the length of the side that is opposite to the angle whose measure is 99.3^(∘). We can use the Law of Sines again!
sin 51/4.7=sin 99.3/y
Let's solve the above equation for y using the Cross Product Property.
