Given:
d = 25
e = 13
f = 16
Let's find the measure m∠D.
The figure below represents this triangle:
To find the measure of angle D, apply the cosine rule:
[tex]d^2=e^2+f^2-2ab\cos D[/tex]
Rewrite the equation for C:
[tex]D=\cos ^{-1}(\frac{e^2+f^2-d^2}{2ef})[/tex]
Where:
e = 13
f = 16
d = 25
Input values into the equation and solve:
[tex]\begin{gathered} D=\cos ^{-1}(\frac{13^2+16^2-25^2}{2(13)(16)}) \\ \\ D=\cos ^{-1}(\frac{169+256-625}{416}) \\ \\ D=\cos ^{-1}(\frac{-200}{416}) \\ \\ D=\cos ^{-1}(-0.4808) \\ \\ D=118.7^0 \end{gathered}[/tex]
Therefore, the measue of angle D is 118.7 degrees.
ANSWER:
d. 118.7 degrees.
