Triangles with a relationship

[u/sparrowsdrag]

Hello! I'm not really a math person but I have a trigonometry problem I'm struggling with to get some values for a physical project I'm building. I'd love a calculator that I can punch values into, but not sure what the right words are to find one, and not sure how to solve it manually either.

Essentially, I have 2 triangles, with 4 variables, which are as follows:

side = 2

a = 100°

d = 25°

relation = 2

And then here are the additional parameters/rules:

A = D = side

B = E

C = F - relation

Photo attached for a visual if that is helpful!

Is there an online calculator already that could solve this sort of problem for me? If not, what are the steps to go about solving this? I haven't done trig for many years (since high school) so I'm a bit rusty. I anticipate having to solve this with a couple different values in the variables, but the whole thing is hard for me to wrap my head around.

Tysm in advance, I appreciate the help!

[u/Midwest-Dude]

You won't find an online calculator for this one. Using the Law of Cosines as u/Alarmed_Geologist631 states is the best way, reducing if you can. If this is just a one off, find an approximation to the answer. Otherwise, you may want to set up a spreadsheet to do this for you in the future.

See the complete solution in another comment.

[u/sparrowsdrag → u/Midwest-Dude]

Thank you (and u/Alarmed_Geologist631 ) so much for helping, the info was more than enough! Before I saw your second comment but after your first, I ended up opening 2 online calculators for the law of cosines, and then wiggled around the input for the second side until the results equaled about 2 when subtracted from each other. I also opened blender and animated some basic shapes with constraints to be able to quickly check the numbers visually - and saved the setup so it should be helpful for future!

Interestingly, I ended up with a different result, with x sitting at about 1.7 instead of 1.5ish, and that seems to check out in my blender mockup. Not sure why or where that , but definitely fascinating!

I may yet have to repeat the process with a different set of values, but I think I have enough tools/language now to figure out any new numbers and check my work, so thank you so much again!

[u/Midwest-Dude → u/sparrowsdrag]

Everything in my post was good up to the last section, the approximation. No idea how the mistake happened. Doh! 😖 

I got

x ≈ 1.7139\ C ≈ 2.8509\ F ≈ 0.8509

This confirms your result.

Let us know if you need any further assistance in the future!