Question

Gustavo and Aiden are walking due west through the forest when they happen upon an angry grizzly bear. Gustavo runs away 2 3 23 ​∘ ​​ 23, degree north of east for 3 0 0 300m300, space, m, and Aiden runs away 3 3 33 ​∘ ​​ 33, degree south of east for 2 5 0 250m250, space, m. How far are Gustavo and Aiden away from each other?

Answer 1

We can actually solve this problem using the cosine law. We know that Gustavo ran 23° above the horizontal, while Aiden ran 33° below, hence the total angle between them is 56°. Therefore the distance between them is:

c^2 = a^2 + b^2 – 2 a b cos θ

c^2 = (300)^2 + (250)^2 – 2 (300) (250) cos 56

c^2 = 68,621.06

c = 262 m

 

They are 262 meters apart.

Answer 2

Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal. So, they are 262 meters apart.

What is a cosine law?

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

Gustavo ran 23° above the east horizontal, while Aiden ran 33° below the east horizontal.

The total angle between them = 23 + 33 = 56°.

Let the distance between them be c. by using cosine law we have,

c² = a² + b² – 2ab cos θ

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

Therefore,

$c^2 = a^2 + b^2 - 2 a b cos \theta$

$c^2 = (300)^2 + (250)^2 -2 (300) (250) cos 56$

$c^2 = 68,621.06$

c = 262 m

Thus, the distance between them is 262 meters.

Learn more about cosine law;

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