Answer:
Option A.) 43°
Step-by-step explanation:
Part 10)
step 1
Find the length of side EG
see the attached figure to better understand the problem
we know that
In the right triangle EGF
[tex]cos(65^o)=\frac{EG}{EF}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(65^o)=\frac{EG}{11}[/tex]
solve for EG
[tex]EG=(11)cos(65^o)\\EG=4.65\ cm[/tex]
step 2
Find the measure of angle D
In the right triangle DEG
[tex]tan(D)=\frac{EG}{DG}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(D)=\frac{4.65}{5}\\\\D=tan^{-1}(\frac{4.65}{5})=43^o[/tex]
