Question

In DEF, d = 25, e = 13, and f = 16.......

Answer 1

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:

`d^2=e^2+f^2-2ab\cos D`

Rewrite the equation for C:

`D=\cos ^(-1)((e^2+f^2-d^2)/(2ef))`

Where:

e = 13

f = 16

d = 25

Input values into the equation and solve:

`\begin{gathered} D=\cos ^(-1)((13^2+16^2-25^2)/(2(13)(16))) \\ \\ D=\cos ^(-1)((169+256-625)/(416)) \\ \\ D=\cos ^(-1)((-200)/(416)) \\ \\ D=\cos ^(-1)(-0.4808) \\ \\ D=118.7^0 \end{gathered}`

Therefore, the measue of angle D is 118.7 degrees.

ANSWER:

d. 118.7 degrees.