Trigonometry Question - Totally Stuck!!

[getrekdent]

Hi all,
I am stuck on a problem that I just can't seem to figure out. It's been a long while since I've done any trigonometry and I've been browsing around the internet for a few hours with zero luck. I am looking to find the area of Area A and Area B in the below screenshot. Can anyone provide a formula and explain to me how it works? I need to build it into an excel program for work to calculate 20,000+ rows of volumetric data. Thank you so much in advance!

 

[Dr.Peterson]

Presumably you see that A and B are congruent triangles, so their areas are the same. You have the angles and one side, the same for each.

I would suggest using the Law of Sines to find one of the other sides of the triangle, and then use the formula K = a b sin(C)/2 for the area.

On the other hand, I find this in a formula table: K = a^2 sin(B) sin(C)/[2 sin(A)]; that uses exactly the information you have, so you don't need to do the work I would have done. (My method derives this formula.)

 

[getrekdent]

Thank you so much for the quick response! I am able to calculate the three angles at each occurrence therefore I am able to use the second method provided. You saved me! THANK YOU!

 

[Dr.Peterson]

Great! For reference, here is the table I found the formula in, though it can probably be found elsewhere.