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Mathematics
Foreverangel:

Find RT 10 m 13m 14 m 16 m

Foreverangel:

1 attachment
Vocaloid:

some notation to introduce: let the three angles of a triangle be capital A, B, and C the side across from <A is a (lowercase a) side across from <B is b, and so on you have: an angle, the side across from it, and another angle, and you want the side across the second angle law of sines sin(A)/a = sin(B)/b you can let <A and a be your known side and angle you can also let <B be the other angle and solve for b

Foreverangel:

I am not really getting it

Vocaloid:

maybe a picture might help? https://i.stack.imgur.com/hKpJj.png

Foreverangel:

Okay yeah that makes a little more sense

Vocaloid:

A, B, and C are just arbitrary labels we can let the 109 degree angle be angle <A, so the side across from it (22m) is a we can let the 34 degree angle be angle <B, so the side across from it is b sin(A)/a = sin(B)/b sin(109)/22 = sin(34)/b should be straightforward from there, make sure your calculator is in degree mode

Foreverangel:

Thank you so much!

Foreverangel:

Hey so when I try to solve it its saying it cant solve the problem

Vocaloid:

what calculator are you using? you could also simply cross-multiply sin(A)/a = sin(B)/b b sin(A) = a * sin(B) b = a * sin(B) / sin(A)

Foreverangel:

I am using Desmos

Vocaloid:

... desmos? isn't that more of a graphing software? if you use a calculator like wolframalpha or mathway you can solve for b https://www.wolframalpha.com/input/?i=sin%28109%29%2F22+%3D+sin%2834%29%2Fb

Vocaloid:

b = a * sin(B) / sin(A) = 22 * sin(34) / sin(109) in order to get this to work on desmos, you need to go to the right hand side, click the wrench icon, change to degree mode since we're in degrees (yeah I wouldn't recommend desmos for trig problems)

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