1. Kelly is playing with her drone, which she got from Santa last Christmas. When she flies her
drone, it reaches a certain height and then falls straight down to the ground. Kelly noticed that
this always happens when she looks up at a 70° angle of elevation to see the drone. When she
goes to retrieve the drone, it is always 250 ft away from where Kelly was standing when it fell
from the sky. What was the maximum height of the drone?

686.86 feet

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Tan α = opposite side / adjacent side

Where α is the angle of elevation of Kelly's view, the opposite side (x) is the maximum height of the  drone, and the adjacent side is the horizontal distance between Kelly and the drone when it hits the ground.

Replacing with the values given:  

Tan 70 = x/ 250  

Solving for x  

tan70 (250)=x

686.86 ft = x

Feel free to ask for more if needed or if you did not understand something.  

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°