the sine rule?

Question

it's probably best to draw it ..
ok there's a triangle labelled ABC

angle C =30degrees
the two other angles are not given

length BA =8.1cm
length AC=7.5cm

calculate the size of angle ABC.
give your answer correct to 3 sig. fig.

i got the answer 0.0376 using the sine rule but it doesn't look right.

i did 7.5/sinB = 8.1/sin30

then i did B= sin8.1/7.5sin30

is this correct? if not, why not?

Answer 1

it should have worked this way

7.5 / sinB = 8.1 / sin30

sinB / 7.5 = sin30 / 8.1

sinB = 7.5 sin30 / 8.1

sinB = (7.5)(.5)/ 8.1 = .463

B = arcsin (.4630) = 27.6 degrees

Answer 2

you have the fraction backwards and it should be the inverse sign

from here
7.5/sinB = 8.1/sin30

cross multiply

8.1(sinB) = 7.5*sin 30

sinB = (7.5*sin30) / 8.1

Take the inverse sign

B = sin^-1(7.5*sin30) /8.1
B = 27.578 degrees (to 3 sig. fig.)

Answer 3

The answer is 27.5784 degrees, because the steps you typed are missing the sine inverse of the final answer.
B = Sin^(-1) (SinC (7.5/8.1))

Answer 4

8.1 sinB=7.5 sin 30
sin B=(7.5 sin 30)/8.1
then you need to use sin^-1
sin B=0.462962963
B=27.6