Question

Calculate the length a to two decimal places.

Answer 1

do you know sin law and cos law

Answer 2

I have notes of it, but it is very confusing the way it is stated.

Answer 3

Cos Law = a^2 + b^2 -2ab(Cos c) = c^2

Answer 4

Sin Law = a/sinA = b/sin B = c/sin c

Answer 5

Alright, I know that is the formula, but I am confused as to what I need to plug in and where

Answer 6

The opposite of ANGLE A should be SIDE a

Answer 7

same with b and c

Answer 8

alright, I'll attempt it right now and report back with what I get

Answer 9

which one do I do first cos law or sin law?

Answer 10

cos law

Answer 11

Could you set the problem up for me? I am very confused

Answer 12

7^2 + 9^2 - 2(7)(9)(cos 117) = c^2

Answer 13

I got 4(cos117)=c^2

Answer 14

okay now take sqrt

Answer 15

For law of sines, you're required to have a corresponding angle and side in order to apply it. So if you have a triangle with sides labeled a, b, c and angles A B C, you must have both a's, both b's, or both c's in order to use it.

In your triangle, you have angle A, side b, and side c. So you clearly dont have a pair. This is why law of cosines would be required for the problem. Now the law of cosines formula can be shifted around depending on the information youhave and what you need to solve for. Because I need side a, I would set up the law of cosines formula in the form:
\[a^{2} = b^{2} + c^{2} - 2bc*\cos(A)\]

Of course you have the work being done right now, but this is just an explanation of why we're doing what we're doing.

Answer 16

And the numbers you have typed up above should be equal to a^2, not c^2

Answer 17

I got 2(cos 117)

Answer 18

a should = 14.874...

Answer 19

\[7^{2} + 9^{2} -2(7)(9)\cos(117) = 130 - 126\cos(117)\]
\[130 - 126\cos(117) \neq 4\cos(117)\]

Answer 20

\[130-126\cos(117) = c^{2} \implies \sqrt{130-126\cos(117)} = c \implies c \approx 13.68\]

Answer 21

Thank you, both!

Answer 22

No problem :)