Question

Use Inverse trig functions to solve for the missing angles

D
8.5
F
E
6.5

Answer 1

Angle <E is approximately 40 degrees, and angle <D is approximately 50 degrees

Explanation:

Since angle <F is clearly 90 degrees, we can find angle E using the cosine function that relates the adjacent side to the angle with the hypotenuse:

`cos(\theta)=(adj)/(hyp) \\cos(E)=(6.5)/(8.5)\\E = arccos((6.5)/(8.5))\\E\approx 40.12^o`

And we use the sin function to deal with angle <D:

`sin(\theta)=(opp)/(hyp) \\sin(D)=(6.5)/(8.5)\\D = arcsin((6.5)/(8.5))\\D\approx 50^o`