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Rufina [12.5K]
3 years ago
9

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 po

int 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?

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
8 0

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 <u>Law of Cosines.</u>

<u />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<u />

<u>The distance from point A to point​ B is 1849.91 feet.</u>

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