Triangle questions ?

Question

In ABC ∠A = 60* , ∠B = 45* and BC= 12cm, Find AC

After I did all the work I figured out that

A= 9.7 cm

C=13.3

Is that the right answer or did I go about finding the answer wrong?

Please help.

10 points

Answer 1

The question just ask you for side AC, not separated. So it's answer 9.80

Answer 2

Judging by the question.

AC should be just the length from A to C.

Probably your 9.7 cm?   or 9.8 (9.79795...?)

Answer 3

AC is the side opposite of ∠B.

According to the sine theorem:

(i) AC / sin(∠B) =BC / sin (∠A)

sin(∠A) = sin (60*) = sqrt(3)/2

Put this into (i), and get that

AC / sin (∠B) = BC / (sqrt(3) / 2)

AC / sin 45* = 2BC / sqrt(3)

AC / (sqrt(2) / 2) = 2 * 12cm / sqrt(3)

sqrt(2) AC = 24cm / sqrt(3) // Multiply by sqrt(3)

sqrt(6) AC = 24cm // divide by sqrt(6)

AC = 24cm * sqrt(6)  / 6 = 9.80cm (approximately).

Answer 4

sin a x b = sin ß x a

a = sin a x b : sin ß

Answer 5

no

12/sin60=x/sin45

x=4sqrt(6)