## kenneyfamily 3 years ago If A=42.2degrees, B= 13.6degrees, and a=41.3, find area of triangle ABC

1. jayz657

we need to see how the triangle looks like otherwise we cant say anything about it

2. zepdrix

|dw:1353222533411:dw| Hmm i don't think it really matters what it looks like :D we have 3 pieces, angle angle side, so we should be able to figure something out. hmmmmmmmm This is not drawn to scale, so my bad :3 just to give us a rough idea. Angle B should be much smaller though :)

3. zepdrix

Area, hmmmmmmmm I'm trying to rememberrrrr :3

4. jayz657

area of triangle = bh/2 how do you know what the height is?

5. kenneyfamily

nope :(

6. zepdrix

We could use the information we have, solve for the missing sides using the law of sines or cosines or something, and then apply heron's formula... I'm not sure that is the most efficient way though XD hehe

7. kenneyfamily

a)138.8 b)327.4 c)493.8 d)246.9 those are my choices

8. Dido525

@zepdrix : Just use Tan to find the height and then use the triangle area formula.

9. Dido525

Ohh wait. It's not a right angle triangle.

10. zepdrix

Yah :c

11. Dido525

Use the law of sines then. Lot easier.

12. Dido525

|dw:1353223094929:dw|

13. Dido525

Solve for b which is the height and then you have everything else.

14. kenneyfamily

36.292 is the height right?

15. kenneyfamily

is 41.3 the base?

16. kenneyfamily

hmm thats not right

17. jayz657

we do not know the height so use this formula Area = 1/2 ab sin(c) we need a side so use law of sines 41.3/sin(42.2) = b /sin(13.6) b = 14.4575 angle c = 180 - 42.2 - 13.6 = area = 1/2(41.3)(14.4575)sin(124.2) area = 246.93 so is D