Height and Distance

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I have the value of X1, X2 and Ө.
Any one can find R (radius)?

Posted 28-Sep-10 22:56pm

Pritesh Aryan

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Sauro Viti · Accepted Answer · 2010-09-28T23:12:00

Solution 1

You have to solve the following equation system:

R * cos(ß) = X2
R * cos(ß + Ө) = X1

Then:

R * cos(ß) = X2
R * (cos(ß) * cos(Ө) - sin(ß) * sin(Ө)) = X1

Now, divide the 2nd equation by the first:

cos(Ө) - tg(ß) * sin(Ө) = X1 / X2

Then:

tg(ß) = (cos(Ө) - X1 / X2) / sin(Ө)

And finally:

ß = arctg((cos(Ө) - X1 / X2) / sin(Ө))
R = X2 / cos(ß)

Posted 28-Sep-10 23:12pm

Sauro Viti

Updated 28-Sep-10 23:14pm

v2

Comments

Pritesh Aryan 29-Sep-10 5:30am

Hello Sauro,

I have does meaning of
tg as TAN or TANGENT
and
arctg as INVERSTAN or INVERSTANGENT

Is It Right?

Thanks........

Sauro Viti 29-Sep-10 5:32am

Yes, it is! tg stays for tangent and arctg stays for arc-tangent (i.e. inverse tangent).

Cheers

Pritesh Aryan 29-Sep-10 6:00am

Thank you so much,

but there is little error,
please improve it with this

ß = arctg(cos(?) - (X1 / X2) / sin(?))
R = X2 / cos(ß)

Thanks...........

Sauro Viti 29-Sep-10 6:16am

mhmm... are you sure? I think it should be (cos(B) - X1/X2) / sin(B) = (cos(B) - (X1/X2)) / sin(B)