Question

Please help! Given a=60, B=42degrees, C=58degrees. Find the area of triangle A B C.
The area= ?

Answer 1

Well, in this case we have 2 angles, and the side between. At least I think so. is that correct?

Answer 2

Yes, I believe so

Answer 3

so A = 80 degrees

Answer 4

I'm not sure if there is a quicker way, but you can use the law of sines to get the other two sides.

Answer 5

a/sin A = b/sin B = c/sin C
Do you know that one?

Answer 6

Oh o.k.

Answer 7

Once you have the sides then you can find the length of an altitude to any one, or use Heron's formula again.

Answer 8

Making sense?

Answer 9

You don't need the law of sines.

Answer 10

Yes. But how would I find the sides to fill in the formula?

Answer 11

You do, sorry.
We have the formula sin(A)/a = sin(B)/b
We know A, B and a
Calculate b

Answer 12

Then use a and angle C to find the altitude down to b
Use b and h to get the area.

Answer 13

Ohhhh thanks! :)

Answer 14

So sin(80)/60=.0164. Now to find altitude I... take 60 and 58?

Answer 15

@telliott99

Answer 16

back

Answer 17

sin 80 deg = 0.985
sin 42 deg = 0.669
sin 58 deg = 0.848
60/0.985 = b/0.669 = c/0.848

b = 40.75
c = 51.65

Answer 18

h/a = sin C
h = 50.9
if I haven't made a dumb mistake.

Answer 19

:/ I can't seem to match up:
a. 1400
b. 2250
c. 1040
d. 1010

Answer 20

I've given you the steps. Somewhere there is a mistake in the arithmetic, or perhaps (unlikely) the problem is in error.

Answer 21

O.k. I'll firgure it out... Thanks!

Answer 22

yw