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A triangle has sides in the ratio of 5:12:13. What is the measure of the triangle's smallest angle in degrees?
Guest Feb 23, 2012
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A triangle has sides in the ratio of 5:12:13. What is the measure of the triangle's smallest angle in degrees?



The ratio is 5:12:13, so assume a base of 1unit, then a triangle with the sides lengths of 5, 12 and 13 fulfills this ratio.

first check if this triangle has one 90deg angle.
Pythagorean theorem:
[input]sqrt(5^2+12^2)[/input]
13 as the length of the third side, so it has 90deg angle.

cos(alpha)=adjacent / hypotenuse
alpha=acos(adjacent / hypotenuse)=acos( 12/13 )

[input]acos( 12/13 )[/input]
about 22deg. (and it is the smallest because 180-90-22=68>22)
admin  Feb 23, 2012

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