Question 74903: The lengths of the sides of a triangle are 7, 8 and 9 cm. Calculate the size of the smallest angle in the triangle (in degrees correct to 2 decimal places).
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The lengths of the sides of a triangle are 7, 8 and 9 cm. Calculate the size of the smallest angle in the triangle (in degrees correct to 2 decimal places).
:
We know the smallest angle will be opposite the smallest side, in this case it
is 7 cm. Also we know it is not a right triangle (Sum of the squares of the 2
smaller sides do not equal the square of the 3rd side)
:
Let the smaller angle be A, then the opposite side = a
a = 7, b = 8; c = 9
:
Use the law of cosines, find the cos of A:
a^2 = b^2 + c^2 - 2bc(cosA)
:
7^2 = 8^2 + 9^2 - 2(8*9)*CosA
:
49 = 64 + 81 - 2(72)*CosA
:
49 = 145 - 144(CosA)
:
+144*CosA = 145 - 49
:
144*CosA = 96
:
CosA = 96/144
:
CosA = .666667
:
A = 48.19 degrees
:
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