Question

Tia climbed to the top of an observation tower overlooking a bird sanctuary and used the telescope at the top to observe two nests. The first nest was 400 meters away from the observation tower. Tia turned the telescope 135 degrees to observe the second nest, which was 300 meters away. How far apart are the two nests?

Answer 1

648 m

Explanation:

Given observations of two nests, one at 400 m, and the other at 300 m in a direction 135° from the first, you want to know the distance between the nests.

Law of Cosines

The law of cosines can be used to find the third side of a triangle, given two sides and the angle between them. It tells us ...

c² = a² +b² -2ab·cos(C)

In this scenario, we have a=400, b=300, and C=135°. The distance c is then ...

c² = 400² +300² -2·400·300·cos(135°) ≈ 419,705.63

c ≈ √419,705.63 ≈ 647.8

The two nests are about 648 meters apart.