Posted by **anon** on Sunday, February 20, 2011 at 11:30pm.

okay so i have this trigonometry problem were i HAVE to use logarithms.

Now this is my work but can u help me solve it using logarithms.

Find the area of the following triangles:(use logarithms)

1) c=426, A=45degrees 48' 36",and B=61degrees 2' 13"

- trigonometry -
**anon**, Sunday, February 20, 2011 at 11:31pm
C = 180 - A - B = 180 - 45° 48' 36" - 61° 2' 13" = 73° 9' 11"

Law of sines: a/sinA = c/sinC

a = c.(sinA/sinC) = 426.(sin(45° 48' 36"))/sin(73° 9' 11"))

a = 426*0.749186

a = 319.153

- trigonometry -
**anon**, Sunday, February 20, 2011 at 11:38pm
i don't know why its asking the url

- trigonometry -
**anon**, Sunday, February 20, 2011 at 11:39pm
anyways the area would be 312,918.8

- trigonometry -
**MathMate**, Sunday, February 20, 2011 at 11:58pm
The length of a is correct.

The area of the triangle would be

A=(1/2)a*c*sin(b)

=(1/2)*319.153*426*sin(61degrees 2' 13" )

=59477.5

I am not able to reproduce your answer for the area.

- trigonometry -
**anon**, Monday, February 21, 2011 at 12:18am
i used cosin and got that answer .. I'm i wrong .

- trigonometry -
**anon**, Monday, February 21, 2011 at 12:25am
is there anyway i can use logarthims in this problem?

- trigonometry -
**MathMate**, Monday, February 21, 2011 at 7:48am
In the old days when there were no calculators, surveying calculations like this would require logarithms to do the multiplications.

There was a book about an inch and a half thick called "7-digit logarithm tables". We would look up sine(61° 2' 13" ) from the table, look up the logarithm of that from another table, then look up the logarithms of 426 and 319.153. These logarithms would have been added together and the anti-logarithm would be the answer: 59477.5.. to 7 digits.

This is the closest relation to logarithm I can think of.

If you want, I can simulate the process.

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