## General Question # Could someone explain this trigonometry question for me?

Asked by dotlin (419 ) July 27th, 2010

http://yfrog.com/5ctrigj
h=d tanθ1 tanθ2 / tan θ2 -tanθ1

I show can’t see how this works out h.

Observing members: 0 Composing members: 0 ## 8 Answers So I’ll explain what I get.

lets replace h:o and d:a tan= o/a but of course we don’t have the full length of a so by rearranging it to o=tanθ a isn’t the right answer so far.

I don’t get why tanθ2 / tan θ2 -tanθ1 is there.

dotlin (419 )“Great Answer” (0 ) Flag as…  Writing out equations is tricky on a keyboard. Can you clarify it a little bit, using explicit parentheses and multiplication signs, so that we can be sure we’re seeing the same equations you are?

MrItty (17376 )“Great Answer” (0 ) Flag as…  I got it in a really roundabout way. I’m going to label “a” as the section of the bottom line that’s to the left of D.

tanθ1 = h/(a+D) and tanθ2 = h/a
I then solved for a in each equation
a = (h – D*tanθ1)/tanθ1 and a = h/tanθ2
Then I set the two a’s equal to each other
h/tanθ2 = (h – D*tanθ1)/tanθ1
Cross-multiply…
h*tanθ1 = h*tanθ2 – D*tanθ1*tanθ2
Put the h’s on the same side of the equation
h*tanθ1 – h*tanθ2 = D*tanθ1*tanθ2
Take out the common factor
h*(tanθ1 – tanθ2) = D*tanθ1*tanθ2
Then solve for h
h = (D*tanθ1*tanθ2)/(tanθ1 – tanθ2)
Voila!

Mariah (25831 )“Great Answer” (1 ) Flag as…  Oh, shoot. This isn’t homework, is it? I probably shouldn’t have helped you quite that much if it was…

Mariah (25831 )“Great Answer” (0 ) Flag as…  No school is out just wanted to know.

dotlin (419 )“Great Answer” (0 ) Flag as…  @Mariah
I’m just having struggle imagining a = (h – D*tanθ1). a = h/tanθ2 is basic trig but a = (h – D*tanθ1) doesn’t feel instinctive at all.

Try and explain that formula in words so it may help me then.

dotlin (419 )“Great Answer” (0 ) Flag as…  Yes everything else seems fine apart from not instinctively getting that, thanks so much so far

dotlin (419 )“Great Answer” (0 ) Flag as…  Start with tanθ1 = h/(a+D)
Multiply both sides by a+D: (a+D)*tanθ1 = h
Distribute: a*tanθ1 + D*tanθ1 = h
Subtract: a*tanθ1 = h – D*tanθ1
Divide: a = (h – D*tanθ1)/tanθ1

Mariah (25831 )“Great Answer” (1 ) Flag as… ## Answer this question or

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