Question

the longest side of a triangle measures 2 and the shortest side measures 1. what cannot be the measurement of the angle between them?
a-30 degrees
b-60degrees
c-70 degrees
d-90degrees

Answer 1

I'd have to go with 90 degrees. That would make them the legs of a right triangle, but the hypotenuse is longer than either leg.

Or, analytically, using the law of cosines, let θ be the angle between the sides, and a be the length of the side opposite θ, and we get

a^2 = 1 + 4 - 4cosθ
cosθ = (5-a^2)/4

Now, we know that 1 < a < 2, so

1/4 < cosθ < 1

So, since cos 90 = 0, it does not fit the bill.