# Am I right, what's your opinion? trigonometry

## Main Question or Discussion Point

a=4, b=1, C=120*

do you agree, that if you do not round until the final amswer, that angle B = 10.90? rounded to the nearest hundredth?

AlephZero
Homework Helper
The cosine rule gives c = sqrt(21).

Sin b = b sin C / c = sqrt(3)/(2 sqrt(21)
= 1 / (2 sqrt(7))

B = 10.8933946491309056054825252598699 according to my calculator.

So you are both wrong Thats what i get too, actually. I just remembered it being 89 and wrote 90 out of memory.

I think the difference is that i used the square root of 21 throughout all calculations rather than 4.38 or whatever it roughly is.

HallsofIvy
Homework Helper
I don't get either of those! I get B= 10.98 degrees.

I assume that you have a triangle in standard notation- a is the side opposite angle A, etc. Since C is the angle between sides a and b, we must first use the "cosine law": $c^2= a^2+ b^2- 2abCos C$
$c^2= 4^2+ 1^2- 2(4)(1)(-0.5)= 16+ 1+ 4= 21$
$c= \sqrt{21}= 4.5826$

Then, by the sine law,
$$\frac{sin(B)}{b}= \frac{sin(C)}{c}$$
$$\frac{sin(B)}{1}= \frac{sin(120)}{4.5826}= \frac{.8660}{4.5826}= 0.18897$$
so that [tex]B= 10.89.

(Oops, a little late!)