Question

Solve the following triangles for all sides and angles:
a=5 b=8 C=40 degrees, what is A, B, and c

Answer 1

Well it would help to see a graphic:

Answer 2

When you know two sides and the included angle, then you use the Law of Cosines to solve the other side and other 2 angles.

Answer 3

I know all of that I just can't figure out how to make it work to get A B and c

Answer 4

Here's how to make it work:
Let's use the 3rd formula in the graphic:
c^2 = a^2 +b^2 - 2ab * cosine C
c^2 = 5^2 + 8^2 -2*5*8 * cosine (40)
Can you solve for side c^2?

Answer 5

okay a = 5 What is a^2?

Answer 6

27.7164

Answer 7

I got 27.7164 but the answer key says it's 5.3 ?

Answer 8

You have correctly calculated c^2
Now what does c equal?

Answer 9

13.8582

Answer 10

If c^2 = 27.7164 then what is c?

Answer 11

13.8582

Answer 12

c is the square root of 27.7164 which is?

Answer 13

5.2646

Answer 14

Correct!

Answer 15

what's A and B then

Answer 16

If you know all 3 sides (which we now do) we can use the Law of Cosines again.

Answer 17

cos A = (b^2 + c^2 - a^2) / 2*b*c

Answer 18

cos A = (8^2 + 5.2646^2 -5^2) / (2 * 8 * 5.2646)
Can you calculate angle A?

Answer 19

I got 1404.9324

Answer 20

cos A = (64 + 17.716 -25) / 84.2336
cos A = 56.716 / 84.2336
cos A = 0.67332

Do you know how to find the arc cosine of A?

Answer 21

wheres the 17.716 from

Answer 22

My mistake
that should be (8^2 + 5.2646^2 -5^2) / (2 * 8 * 5.2646)

= (64 + 27.716 - 25) / 84.2336
= 66.716 / 84.2336
=0.7920354823

can you find the arc cosine of 0.7920354823?

Answer 23

Here's a good online trig calculator http://www.1728.org/trigcalc.htm
Now can you calculate the arc cosine of .7920354823?

Answer 24

Did you go to the online trig calculator?

Answer 25

i got 37.6238 idk

Answer 26

That is correct!
Now (and finally) the LAST thing to do is calculate the third angle which is quite easy

Answer 27

102.3762

Answer 28

Precisely!! Now you see how it is done!

Answer 29

thank you

Answer 30

u r welcome :-)