Question

Consider a triangle with side lengths of 10 ft, 17.32 ft, and 20 ft. By examining the side lengths, what can you conclude about the measurement of the angles? Explain your reasoning. A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3 . B) The angles are 60-60-60. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3. C) The angles are 45-45-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3. D) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 2.

Answer 1

A) The angles are 30-60-90. The longest leg (hypotenuse) of the triangle is twice the shortest leg. The middle leg is the shortest leg times the square root of 3.

Explanation:

The answer choice speaks for itself.

The legs of a 45-45-90 triangle have the ratios 1 : 1 : √2.

The legs of a 30-60-90 triangle have the ratios 1 : √3 : 2.

Clearly, the given leg lengths match the second set of ratios more closely:

10 : 17.32 : 20 ≈ 1 : √3 : 2.