Question

Which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle? Check all that apply.

A. 13:15
B. 1 : 2
C. 2:15
D. 1:3
E. 15:3
F. 1 : 15

Answer 1

The ratios between the lengths of the legs in a 30-60-90 triangle are always consistent, with the shorter leg to hypotenuse ratio being 1:2 and the longer leg to hypotenuse ratio being 1:√3.

Step-by-step explanation:

A 30-60-90 triangle is a special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The ratios between the lengths of the sides in a 30-60-90 triangle are always consistent.

The ratio between the length of the shorter leg and the hypotenuse is 1:2, the ratio between the length of the longer leg and the hypotenuse is 1:√3, and the ratio between the length of the shorter leg and the longer leg is √3:2.

Therefore, the ratios that could be between the lengths of the two legs of a 30-60-90 triangle are B. 1:2 and E. 15:3.