Should the triangle be solved beginning with Laws of Sines or Laws of Cosines. Then solve the triangle and round to the nearest tenth. a=16, b=13, c=10

Yes. I have no idea what the question is.

Whether the law of cosines or the law of sones be used first to solve for the triangle

If you are given three sides, start with the law of cosines to get one angle. Then you may go to the law of sines to get the second angle, then the third angle is solved by knowing the sum of the interior angles of a triangle is 180deg.

I got this answer wrong but don't understand where I made the mistake.

a=16, b=13, c=10

a^2=b^2+c^2-2bc Cos A
16^2=13^2+10^2-2(13)(10) Cos A
16^2-13^2-10^2/-2(13)(10)=-2(13)(10)/-2(13)(10)
-13/-260 Cos A = 0.05=Cos A = 152=A

sinB/b=SinA/a
Sin B/13=Sin152/16
Sin B = 13 Sin 152/16

To determine whether to use the Laws of Sines or the Laws of Cosines to solve a triangle, you need to examine the given information.

The Laws of Sines apply when you have either two angles and one side (AAS or ASA), or two sides and a non-included angle (SSA). In such cases, you can use the formula:

sin(A) / a = sin(B) / b = sin(C) / c,

where A, B, and C are the angles, and a, b, and c are the corresponding sides opposite those angles.

On the other hand, the Laws of Cosines are used when you have the three sides of a triangle (SSS) or when you have one side and two angles (SAS). The formula to solve the triangle using the Laws of Cosines is:

c^2 = a^2 + b^2 - 2ab * cos(C),

where c is the side opposite angle C, and a and b are the other two sides.

In the given triangle with sides a = 16, b = 13, and c = 10, we have three sides (SSS). Therefore, we should use the Laws of Cosines to solve the triangle.

To find angle C, we can use the Law of Cosines formula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Substituting the given values, we get:

10^2 = 16^2 + 13^2 - 2 * 16 * 13 * cos(C)

Simplifying further:

100 = 256 + 169 - 416 * cos(C)

269 - 356 = -416 * cos(C)

-87 = -416 * cos(C)

cos(C) = -87 / -416

cos(C) = 0.2091355 (rounded to seven decimal places)

To find angle C, we can take the inverse cosine (arccos) of the value we obtained:

C = arccos(0.2091355)

C = 78.7812877 degrees (rounded to seven decimal places)

Now, we can use the Law of Sines to find angles A and B:

sin(A) / a = sin(C) / c

Substituting the known values:

sin(A) / 16 = sin(78.7812877) / 10

Simplifying:

sin(A) = (16 / 10) * sin(78.7812877)

sin(A) = 1.6 * 0.9781476

sin(A) = 1.5650361

Now, we can find the inverse sine (arcsin) of the obtained value:

A = arcsin(1.5650361)

A = 92.4927132 degrees (rounded to seven decimal places)

Since the sum of angles in a triangle is always 180 degrees, we can determine angle B by subtracting angles A and C from 180:

B = 180 - A - C

B = 180 - 92.4927132 - 78.7812877

B = 8.7269991 degrees (rounded to seven decimal places)

Therefore, the solution to the triangle with sides a = 16, b = 13, and c = 10 is:

Angle A: 92.5 degrees
Angle B: 8.7 degrees
Angle C: 78.8 degrees