Question

Find RT

10 m

13m

14 m

16 m

Answer 1

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

Answer 2

I am not really getting it

Answer 3

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

Answer 4

Okay yeah that makes a little more sense

Answer 5

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

Answer 6

Thank you so much!

Answer 7

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

Answer 8

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)

Answer 9

I am using Desmos

Answer 10

... 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

Answer 11

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)