Question

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 1

Answer: 29.8ft

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