# Cosine Law Problem

• Mar 17th 2013, 04:48 PM
Mathnood768
Cosine Law Problem
The longest tunnel in North America could be built through the mountains of the Kicking Horse Canyon, near Golden, British Columbia. The tunnel would be on the Trans-Canada highway connecting the Prairies with the west coast. Suppose the team selected point A, 3000m away from the proposed tunnel entrance and 2000m away from the tunnel exit. If angle A is measured 67.7 degrees, determine the length of the tunnel.

So, I tried doing this question using the formula:

a^2 = b^2 + c^2 - (2)(b)(c)cosA

I drew a diagram of how I think the problem would look like aswell:

http://i.snag.gy/kOPLN.jpg

My attempt:

a^2 = b^2 + c^2 - (2)(b)(c)cosA

a^2 = 2000^2 + 3000^2 - (2)(2000)(3000)cos67.7

a^2 = 13000000 - 12000000cos67.7

a^2 = 1000000cos67.7

a^2 = 379456.1595

a = 616 m

The answer is suppose to be 2906 m... I'm not sure what I did wrong... Any feedback would be great, thanks.
• Mar 17th 2013, 05:57 PM
Paze
Re: Cosine Law Problem
Hi Mathnood768.

Your calculations are right. You are stumbling in the arithmetic.

For proof that your calculations are right, see: sqrt&#40;2000&#94;2&#43;3000&#94;2-2&#42;2000&#42;3000&#42;cos&#40;67.7&#41;&#41; - Wolfram|Alpha