How do you find all the measures of the angles in a triangle that have the ratio of 1:3:5?

1 Answer
Alan P.
Mar 6, 2017

If the given ratio is to be the ratio of the sides:
color(white)("XXX")No such triangle is possible.
If the given ratio is to be the ratio of the angles:
color(white)("XXX")The angles are 20^@, 60^@, and 100^@

Explanation:

Case 1: ratio is ratio of lengths of sides
The length of the two shorter sides of a triangle must be greater than the length of the third side.

Case 2: ratio is ratio of angles
If the smallest angle is x^@
then the ratio 1:3:5 corresponds to angles x^@, 3x^@, and 5x^@

Since the sum of interior angles of a triangle is 180^@
color(white)("XXX")x+3x+5x=180

color(white)("XXX")rarr 9x=180

color(white)("XXX")rarr x=20

and the angles are 20^@, 60^@, and 100^@

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