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September 4, 2015

Homework Help: math

Posted by Jessica on Tuesday, July 5, 2011 at 4:23am.

This is the problem given: The side of a hill faces due south and is inclined to the horizontal at an angle alpha. A straight railway upon it is inclined at an angle beta to the horizontal. If the bearing of the railway is gamma east of north, show that cos(gamma) = cot(alpha)tan(beta)

I drew a diagram like this, according to this question (imageshack.us/photo/my-images/30/trigonometryquestion.png/).
We have cos(gamma) = CH/AC
cot(alpha) = BH/CH
tan(beta) = CH/AH,
so cot(alpha)xtan(beta) = BH/AH
I'm stuck at proving CH/AC = BH/AH

Is there anyway around this? I'll appreciate any help from you all. Thank you very much.

Note: AC is not perpendicular to BC.

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