The lengths of the sides of a triangle are 7, 8 and 9 cm. Calculate the size of the smallest angle in degrees?

Question

The lengths of the sides of a triangle are 7, 8 and 9 cm. Calculate the size of the smallest angle in degrees?

Answer 1

Well the smallest angle is opposite the smallest side. Then use one of your trig properties and set up the ratio.  

Answer 2

go-go gadget law of cosines.

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Let x be the smallest angle, then since it is opposite the smallest side (of length 7), the law of cosines states:

7^2 = 8^2 + 9^2 - 2*8*9cos(x)

Or solving for cos(x):

cos(x) = (8^2 + 9^2 - 7^2) / (2*8*9) = 2/3.

x = arccos(2/3)

which is about 48.189685 degrees.

Answer 3

You need at least two other angles.

Law of sines

Sin A / a  = Sin B / b = Sin C / c

"A , B, C" are angles; "a, b, c," are sides

You need at least one other angle to simplify the proportion.

Awms A says use law of cosines; that won't work. {c^2 = a^2+b^2 -2ac Cos C}