Triangle of RST , Big R =105degrees,r =9,s=6.

Question

What is S T and t

Answer 1

By sine rule, we have:

r / sinR = s / sinS
9 / sin(105) = 6 / sinS
sinS = 6 / (9 / sin(105))
sinS = 0.64395055
S = sin^-1 (0.64395055)
S = 40.08703691 degrees

By sum of interior angles of a triangle, we have:

R + S + T = 180
105 + 40.08703691 + T = 180
T = 180 - 105 - 40.08703691
T = 34.91296309 degrees

Using sine rule again, we have:

r / sinR = t / sinT
9 / sin(105) = t / sin(34.91296309)
t = (9 / sin(105)) * sin(34.91296309)
t = 5.33268975