Question

A triangle has sides a b c and angles A B C. If angle A is 81, side a is 11 and side b is 12, what is angle B?

Answer 1

use cosine law.

Answer 2

Do what shubham says: cosine rule.

Answer 3

i.e.
\[b^{2}=a^{2}+c^{2}-2ac cosB\]

Answer 4

But I don't know what side c is?

Answer 5

So I have two unknowns

Answer 6

first find c.

Answer 7

using cosine law,
\[c^{2}=a^{2}+b^{2}-2ab cosC\]

Answer 8

Sorry, I don't know angle C either...should I use sine rule instead?

Answer 9

oh sorry,
you can use sine law,

Answer 10

\[\frac{sinA}{a}=\frac{sinB}{b}=\frac{}{}\]

Answer 11

So...sin A/a = sin B/b, which would be sin 81/11 = sin B/12

Answer 12

So (12 sin 81)/11 = sin B.

sin B = 1.077

Answer 13

But my calculator gives an error message when I try to find sin -1 of 1.077 - shouldn't values of sin be less than 1?

Answer 14

Have I gone wrong somewhere?

Answer 15

no , i am also getting 1.077
there would be problem with given data

Answer 16

Oh...I just double checked the numbers on the question, and I didn't copy them wrongly...the question asks if there are two possible values for angle B, so perhaps it's a trick question and this one has no possible solutions....hmm, not sure. Thanks for your help anyway.

Answer 17

:)

Answer 18

Hi @Kashan, how did you get sin B = 12/11? Did you use sine rule?