Question

Which one of the following cannot be the ratio of angles in a right-angled triangle?
(1) 1: 2 : 3 (2) 1 : 1 : 3 (3) 1 : 3 : 6 (4) None of these
(also plz provide some insight on how to calculate this)

Answer 1

An important piece of information: in a right-angled triangle, the right angle is ALWAYS the largest angle. Take the first one for example: (1) 1 : 2 : 3
3 is the largest number, so it refers to 90 degrees. The 1, and 2 therefore must refer to 1/3, and 2/3 of 90 degrees respectively. Do they all add to 180 degrees? (another qualifying factor of a triangle) Well sure they do:
\[\frac{1}{3} \times 90 = 30\]\[\frac{2}{3} \times 90=60\]\[30+60+90=180\]So (1) can be a right-angled triangle.

Answer 2

considering the second option, the first ratio comes to 30, and 30, the last 90? is this right?

Answer 3

That's right, yep. Does their sum equal 180?

Answer 4

no (comes to 120), but the right answer given is the 3rd option