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need help with area of triangles & logarithms

need help with area of triangles & logarithms

QUESTION: If  you  are asked to find the area of a triangle and use logarithms.how could you use logarithms to find the area , if these are oblique triangles ?Please list for all of the following conditions.all of these are known factors1.       2 angles & a side of a triangle2.       2 sides & the included angle  3.       3 sides of a triangleI would like to think that I could just convert an area formula into logarithm form.Only problem is, I'm not 100% for sure if this is correct.FOR EXAMPLE:        Let's say we  need to find the area of a right triangle .formula :      A=1/2*base*heightIn log form may be changed to ??       logA= log1-log2+log base+log heightIf not please show how this should be.Then for 1. formula : K= c^2*(sinA)*(sinB)/2*(sinC)can be changed to ??      logK=log(a+b)+log(a+b)+log sin A+log sin Blog2+log sin C K=a^2*(sinB)*(sinC)/2*(sinA)logK=log(c+b)+log(c-b)+log sinB+log sinC-log2+log sinAthen for 2.K=b*c*(sinA)/2    can be changed to ??       logK=log b+log c+log sinA-log 2K=a*b*(sinC)/2  can be changed to ??       logK=log a+log b+log sinC-log 2then for 3. K=the radical sign over   s(s-a)*(s-b)*(s-c)How can I use Heron's formula with logarithms when it contains a radical sign?All hints & pointers are greatly appreciated. Thanks!  :-)
1 REPLY 1

need help with area of triangles & logarithms

On 9/30/00 12:17:14 AM, Anonymous wrote:
>QUESTION: If you are asked to find the area of
>a triangle and use logarithms...

This seems rather artificial to me. The value of the exercise is (I guess) to practise using the fact that

log(a*b) = log(a) + log(b)

log(ab) = b*log(a)

>K=the radical sign over s(s-a)*(s-b)*(s-c)
>How can I use Heron's formula with logarithms
>when it contains a radical sign?

Remember, sqrt(x) is the same as x1/2, hence

log(sqrt(x)) = (1/2)*log(x).

Bonnie
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