Word problem below... I got 39.8 degrees. Can anyone check me answer?

Question

A triangle has sides of lengths 9, 10, and 11. Then the number of degrees in the smallest angle of this triangle, correct to the nearest tenth of a degree, will be

Answer 1

Let's denote a = 9, b = 10, and c = 11, for the sides of the triangle.
Let's also denote A as the angle opposite from side a, B as the opposite angle from side b, and C as the opposite angle from side c.

The smallest angle will be angle A, since the smallest side is a.

By the cosine formula,

a^2 = b^2 + c^2 - 2bc cos(A), so

cos(A) = (a^2 - b^2 - c^2) / (-2bc)

Plugging in our values,

cos(A) = (9^2 - 10^2 - 11^2) / [-2(10)(11)]
cos(A) = (81 - 100 - 121) / [-220]
cos(A) = (-140)/(-220)

Therefore, in its reduced fractional form

cos(A) = 7/11

To solve for A, we take the arccos, or cos inverse, of both sides.

A = arccos(7/11)

This is approximately equal to

arccos(7/11) ~= 50.48 degrees

The "~=" means "approximately equal to", and is normally written as two squigglys as an equal sign.

Answer 2

Cosine rule from trigonometry:

Cos A = (b*b + c*c - a*a) / (2*b*c)
Cos B = (a*a + c*c -b*b) / (2*a*c)
Cos C = (b*b + a*a - c*c) / (2*b*a)

A is the angle opposite side a, B is the side opposite side b and C is the angle opposite side c.

If a = 9, b = 10 and c = 11,

We get:

Cos A = (100 + 121 - 81) / (2 * 10 * 11) = 140 / 220 = 0.63636
Cos B = (81 + 121 - 100) / (2 * 9 * 11) = 102 / 198 = 0.515151
Cos C = (81 + 100 - 121) / (2 * 9 * 10) = 60 / 180 = 0.3333

Taking Cosine inverse, we get
A = 50.5
B = 59
C = 70.5

Therefore, the number of degrees in the smallest angle of the triangle is 50.5 degrees. How did you get to 39.8?

Answer 3

Arg, I cannot check ye answer, but I will steal ye dubloons.

Answer 4

36.6??