Question

The given measurements may or may not determine a triangle.
B = 137°, c = 6, b = 11

Answer 1

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.

Answer 2

@Loser66 @hartnn @amistre64
Anybody? :(

Answer 3

well looking at the information you know b is the longest side since its opposite the largest angle B.

well the law of sines says

\[\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}\]

you have B and b and c

so

\[\frac{\sin(137)}{11} = \frac{\sin(C)}{6}\]

so angle C = 21.84 degrees.

So by angle some of a triangle angle A = 21.16

find side a by the law of sines... and it should be smaller than side c

\[\frac{11}{\sin(137)} = \frac{a}{\sin(21.16)}\]

a = 5.82

now check that

a + c > b

6+ 5.8 > 11

true so you have a triangle.

Answer 4

Thanks campbell! So much help in just one reply