Gustavo and Aiden are walking due west through the forest when they happen upon an angry grizzly bear. Gustavo runs away 23^\circ23 ∘ 23, degrees north of east for 300 \,\text{m}300m300, start text, m, end text, and Aiden runs away 33^\circ33 ∘ 33, degrees south of east for 250 \,\text{m}250m250, start text, m, end text. How far are Gustavo and Aiden away from each other?

They are 261.96 meters apart.

Step-by-step explanation:

From the question, considering a North, East, South and west pole, Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.

Thus, the total angle between them is 23 + 33 = 56°.

Therefore, let the distance between them be c and we can calculate that using the cosine law. Thus,

c² = a² + b² – 2ab cos θ

Where a and b are distances travelled respectively by Gustavo and Aiden. While θ is the angle between them.

Thus,

c² = 300² + 250²– 2(300) (250)cos 56

c² = 90000 + 62500 - 83878.9355

c² = 68621.0645

c = √68621.0645

c = 261.96 m

They are 261.96 meters apart.

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)