# Thread: Problems with Sine Rule Calculations

1. ## Problems with Sine Rule Calculations

Hi everyone,

I am working with the Sine Rule at the moment, where you need to solve the Sine Rule equation to find the value of the unknown side of the triangle. However, although I believe my methods for solving the equation are sound, after performing the calculations themselves, I am left with answers that are sometime a far cry from the correct answer.

Here is an example:

I have a triangle with sides MNP. M has an angle of 38 degrees, N has an angle of 80 degrees and P has an angle of 62 degrees. We're given one unknown "x", and one side length which corrosponds to angle N and has a value of 35.3.

Here is an attachment with a sketch of the triangle:

Now, the Sine Rule is:

a / Sin A = b / Sin B

So, I put my values in and get:

x / sin 38 = 35.3 / sin 80

I rearrange the equation:

x = (35.3 / sin 80) x sin 38

x = 16.76

The correct answer ought to be: x = 22.1

I've checked numerous times to ensure my calculator is in degrees mode.

Any help resolving this will be greatly appreciated!

Thanks,

Nathaniel

2. Really? You must be doing something wrong with your calculator...

I typed in $\displaystyle x = (\frac{35.3}{\sin 80}) \times \sin 38$ and i got $\displaystyle x = 22.068114...$ in degrees mode.

In radians, i got $\displaystyle x = -10.5261...$

I'm not sure how you are getting 16.67.

3. Hi!

It is probably the way you entered it in the calculator. Your equations are correct.

Check this:

(35.3sin38) = 21.7328...

21.328.../sin80 = 22.068...

4. Ah. Thanks for the quick aid Gusbob, and Educated! It WAS just a calculator problem. I didn't realize you have to put the 38 and the 80 before the sine sign (with the online and inbuilt Microsoft calculators that I am using).

Cheers!