Question

A tunnel is planned through a mountain to connect points A and B on two existing roads. If the the angle between the roads at point C is 52degrees​, the distance between points A and C is 2200 ​ft, and the distance between points B and C is 2000 ​ft, what is the distance from point A to point​ B?

Answer 1

Answer:

1849.91ft

Step-by-step explanation:

The problem is represented in the attached triangle.

Our goal is to determine |AB| in the triangle.

Using Law of Cosines.

$c^2=a^2+b^2-2abCosC\\c^2=2000^2+2200^2-2(2000)(2200)Cos52^0\\c=\sqrt{2000^2+2200^2-2(2000)(2200)Cos52^0} \\c=\sqrt{3422179.0171}\\ c=1849.91ft\\|AB|=1849.91ft$

The distance from point A to point​ B is 1849.91 feet.