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 start by finding m∠ E. Then, we will use the above law to find the values of d and f. We will find them one at a time.
From the Triangle Angle Sum Theorem we know that the sum of the angles in a triangle is equal to 180^(∘). With this information we can find E.
m ∠ E + 39^(∘) + 34^(∘) = 180^(∘) ⇕ m∠ E = 107^(∘)
Finding d
Let's mark the measure of the angle E on the graph.
We know that the length of a side is 12 and that the measure of its opposite angle is 107^(∘). We also know that the measure of the angle that is opposite to the side we want to find is 39^(∘). With this information and using the Law of Sines, we can write an equation in terms of d.
sin 39^(∘)/d=sin 107^(∘)/12
Let's solve the above equation for d using the Cross Product Property.
Consider the given triangle with the new information.
We know that the length of a side is 12 and that the measure of its opposite angle is 107^(∘). We want to find the length of the side that is opposite to the angle whose measure is 34^(∘). We can use the Law of Sines again!
sin 107^(∘)/12=sin 34^(∘)/f
Let's solve the above equation for f using the Cross Product Property.
