Lila flies a drone in the direction of 90° towards Avery. Once she gets to Avery she changes course and flies in the direction of 200° towards Mark. Lila and Avery are 20 feet apart; Mark and Avery are 30 feet apart. How far apart are Mark and Lila?

Answer: 29.8ft

Step-by-step explanation:

suppose that the angles are measured from an x-axis.

we know that:

Lila and Avery are 20 feet apart.

Mark and Avery are 30 feet apart.

If we locate the position of Lila in the (0, 0)

and we use the relation:

x = r*cos (θ) and y = r*cos (θ)

Then the position of Avery is:

P = (20ft*cos (90°), 20ft*sin (90°)) = (0, 20ft)

and the position of mark will be:

P = (0 + 30ft*cos (200°), 20ft + 30ft*sin (300)) = (-28.2ft, 9.7ft)

And because Lila is at the origin, the distance between Mark and Lila is equal to the module of that vector,

Distance = √ ((28.2ft) ^2 + (9.7ft) ^2) = 29.8ft