a. law of sines
b. basic trig
c. law of cosines
d. pythagreans therom
how would you figure out which one to use ??
2007-08-30 02:06:31 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
You have 3 sides and biggest angle is opposite the biggest side.
Let biggest angle = θ
By Cosine Rule:-
7² = 5² + 3² - (2 x 5 x 3 x cos θ)
49 = 34 - 30 cos θ
30 cos θ = - 15
cos θ = - 1/2
θ = 120 °
2007-09-03 02:12:08 · answer #1 · answered by Como 7 · 0⤊ 0⤋
Sorry for both answers above, the correct answer is c. You have cos(betha) = (3^2 + 5^2 - 7^2)/(2*3*5) = -15/30 = - 1/2 and betha = 120 degrees. This is the easiest!
P.S.(Edit - how would you figure out which one to use ??) Usually the law of cosines is applied when you have 3 sides /as the case is/ or 2 sides and angle in-between; the law of sines normally requires a side and 2 angles; Pythagorean theorem is applied having a right triangle (this isn't, look the numerator in the above expression!).
2007-08-30 09:14:44 · answer #2 · answered by Duke 7 · 0⤊ 0⤋
Assuming a is the side opposite angle A, and so forth, then it would be a) the law of sines. sin(A)/a = sin(B)/b = sin(C)/c, so the sines of the angles are proportional to the lengths of the sides, and larger angles have larger sines, up to 90 degrees, so A must be the largest angle. If A is larger than 90 degrees, it still holds that this angle corresponds to the largest side, because the sum of all three angles must be 180 degrees, which means that each other angle must still have a smaller sine than that of A, or else the angles couldn't fit in the triangle.
Really, you could use the law of cosines, too, but it's more work. However, if you need to find the measure of the angle, rather than just identify which one is largest, it's the way to go.
2007-08-30 09:14:02 · answer #3 · answered by DavidK93 7 · 0⤊ 0⤋
You can't use the Pythagorean Theorem if it's not a right triangle (is it a right triangle?).
If you have all the sides, or if you have a side and it's corresponding opposite angle, you can use the law of sines. It's probably the simplest way to go.
2007-08-30 09:17:26 · answer #4 · answered by rathrhadit 4 · 0⤊ 0⤋
Law of Sines to find the biggest angle.
Law of Cosines to evaluate the biggest angle.
2007-08-30 10:04:30 · answer #5 · answered by Mark 6 · 0⤊ 0⤋
Looking at a,b,c: they fail the pythogorean test, so this is NOT a right triangle so law of sines and cosines goes out the door. d is not applicable.
Your answer is B.
Most likely the angle opposite side b since it is the longest.
2007-08-30 09:16:50 · answer #6 · answered by Ac 1 2 · 0⤊ 0⤋