Should the triangle be solved beginning with Law of Sines of Law of Cosines. Then solve the triangle. Round to the nearest tenth. a=16, b=13, c=10.
Cosines
A=93 degrees, B=54 degrees, C=33 degrees
no, two of the angles are wrong.
I found this by doing a simple check
sin93/16 , sin54/13 and sin33/10 should be the same within about 2 decimal places even allowing for your roundoff.
They are not!
A good rule to follow when all 3 sides are known, is to find the largest angle by the Cosine Law.
Your calculator has been programmed to give you the correct second quadrant angle if the cosine is negative.
so 16^2 = 13^2 + 10^2 - 2(10)(13)cosA
cosA = (169+100-256)/260 = .05
A = 87.13
Now you can safely use the Sine Law to find one of the other angles, say B
sinB/13 = sin87.13/16
sinB = .81148
B = 54.2 and using the 180º sum property
C = 38.6
Only at this stage would I round off my answers.
To solve a triangle, you can use either the Law of Sines or the Law of Cosines, depending on the information given. In this case, if you are given the lengths of the sides (a, b, c), it is more appropriate to use the Law of Cosines first to find the angles, and then use the Law of Sines to find the remaining side lengths.
Here's how you can solve the triangle:
Step 1: Use the Law of Cosines to find the angles.
The Law of Cosines states that for any triangle with side lengths a, b, and c, and opposite angles A, B, and C, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
Given that a = 16, b = 13, and c = 10, we can substitute these values into the equation to find the angles.
For angle C:
10^2 = 16^2 + 13^2 - 2 * 16 * 13 * cos(C)
100 = 256 + 169 - 416 * cos(C)
229 = -416 * cos(C)
cos(C) = -229 / 416
C = arccos(-229 / 416)
C ≈ 121.8 degrees
Similarly, you can find angles A and B using the Law of Cosines. After calculating these angles, you'll find A ≈ 93 degrees and B ≈ 54 degrees.
Step 2: Use the Law of Sines to find the remaining side lengths.
The Law of Sines states that for any triangle with side lengths a, b, c, and opposite angles A, B, and C, the following equation holds:
a / sin(A) = b / sin(B) = c / sin(C)
Using this equation, you can find the remaining side lengths.
To find side a:
a / sin(A) = c / sin(C)
16 / sin(A) = 10 / sin(121.8)
sin(A) = 16 * sin(121.8) / 10
A ≈ arcsin(16 * sin(121.8) / 10)
Similarly, you can find the lengths of sides b and c using the Law of Sines.
Finally, round the side lengths to the nearest tenth.
So, to answer your question, in this case, you should start by applying the Law of Cosines to find the angles, and then use the Law of Sines to find the remaining side lengths.