Question

Anyone here understand the Law of Sines and Cosines??? I'm completely lost and might need some help throughout my geometry course

Answer 1

why not choose an example problem or two and post it here? I could help much better with a specific problem than with a general "Law of Sines, Law of Cosines" mention.

Answer 2

I only remember the law of sines.

Answer 3

One like this:
A large triangular flag is in the shape of ΔABC, where AB=8.7ft, BC=12.3ft, and AC=15.2ft.

What is the measure of the angle at A, to the nearest degree?

Answer 4

Or:
A traffic helicopter flies x miles in a straight line from point A to point B. It then turns 85° clockwise at point B and continues another y miles in a straight line to point C. The path of the helicopter is shown below.

Which expression gives the distance from point C back to point A, in miles?

\[\sqrt{x2+y2−2xycos(85°)} \]

\[\sqrt{x2+y2+2xycos(85°)} \]

\[\sqrt{x2+y2−2xycos(95°)} \]

\[\sqrt{x2+y2+2xycos(95°)} \]

With the image below:

Answer 5

I don't remember the law of cosines. That's what is needed here I think. @mathmale is a maths professor! :D

Answer 6

supposing that you had a triangle with angles A, B and C and sides a, b and c, with side a opposite
Angle A, side b opposite Angle B, and so on, and you know Angle A and sides b and c. Here's the formula for calculating the square of the length of side a:

\[a^2=b^2+c^2-2bc*\cos A\]

Answer 7

there are 2 other forms, one for b^2 and one for c^2, that follow the same pattern exactly.

Why not draw the triangle in question, labeling everything, and choosing the proper form of the Law of Cosines to apply?

Answer 8

That's a GREAT diagram. Thanks! Here's what you need to find Angle A: it follows your formula.

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Answer 9

Once you have a numeric value for cos A (it must be between -1 and 1), just use the inverse cosine function to find A itself. Want A in degrees or in radians?

Answer 10

So:

151.29 = 231.04 + 75.69 - 264.48 cos A
151.29 = 306.73 - 264.48 cos A
-306.29 -306.29
-155 = -264.48 cos A
----- ------------
-264.48 -264.48
0.58605 = cos A
cos^-1 (0.58605) = 54.12

Right?

Answer 11

And thank you so much for helping me @mathmale :DD

Answer 12

My pleasure! You've done a very nice job of sharing your work.

Answer 13

Let me know if you have further questions about the Law of S. or the Law of C.