EXPLANATION
Since we have the △CDE,let's represent the triangle:
We can apply the law of sines to get the value of the angle C, and then by the Sum of Interior Angles of a Triangle Theorem, we can get the value of the angle D as shown as follows:
[tex]\frac{\sin C}{DE}=\frac{\sin E}{CD}[/tex]
Substituting terms:
[tex]\frac{\sin C}{5}=\frac{\sin 83}{12}[/tex]
Isolating sin C:
[tex]\sin C=5\cdot\frac{\sin 83}{12}[/tex]
Applying sin^-1 to both sides:
[tex]C=\sin ^{-1}(5\cdot\frac{\sin 83}{12})[/tex]
Computing the terms:
[tex]C=\sin ^{-1}(0.4135)[/tex]
Computing the argument:
[tex]C=24.43\text{ degre}es[/tex]
Finally, by applying the Sum of Interior Angles of a Triangle Theorem, we can get the value of D as shown as follows:
C + D + E = 180
24.43 + D + 83 = 180
Isolating D:
D = 180 - 83 - 24.43
Subtracting numbers:
D = 72.57 ≈ 72.6 degrees
