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# The sides of a triangle have side lengths equal to a,band a2−ab+b2−−−−−−−−−−√. What is the measure of the angle ( in degrees) between the longest and shortest side?

Aman Bansal
592 Points
8 years ago

Dear Samyak,

A 30-60-90 right triangle has angles measuring just what the name says. The two acute, complementary angles are 30 and 60 degrees. These triangles are great to work with, because the angle measures, all being multiples of 30, have a pattern, and so do the measures of the sides (though a different pattern).

The Pythagorean theorem also applies in a 30-60-90 triangle — you have that relationship between the squares of the sides. But ab, and c are related in another way, too. In a 30-60-90 right triangle, ifa is the shortest side, then the hypotenuse, the longest side, measures twice that, or 2a. You can use 2a instead of the letter c.

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Thanks

Aman Bansal

saiomkar kandukuri
33 Points
8 years ago

just apply cosine rule amd the answer is(180-(largest +small angle)