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

#1**0 **

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)

Guest: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)

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Feb 23, 2012