Question

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

11 cm
A.) 43°
B.) 5°
C.) 25°
D.) 63

Answer 1

Option A.) 43°

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)=(EG)/(EF)` ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

`cos(65^o)=(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)=(EG)/(DG)` ----> by TOA (opposite side divided by adjacent side)

substitute the given values

`tan(D)=(4.65)/(5)\\\\D=tan^(-1)((4.65)/(5))=43^o`