Question

10) Find the measure of angle D. Hint: you must do two math problems to solve

Answer 1

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

$cos(65^o)=\frac{EG}{EF}$ ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

$cos(65^o)=\frac{EG}{11}$

solve for EG

$EG=(11)cos(65^o)\\EG=4.65\ cm$

step 2

Find the measure of angle D

In the right triangle DEG

$tan(D)=\frac{EG}{DG}$ ----> by TOA (opposite side divided by adjacent side)

substitute the given values

$tan(D)=\frac{4.65}{5}\\\\D=tan^{-1}(\frac{4.65}{5})=43^o$