Question

Construct a 30, 60, 90-degree triangle with the short leg equal to AB. (Hint: In a 30, 60, 90 triangle, H=2S)

a. AB = S, AC = 2S, BC = √3S
b. AB = S, AC = S√3, BC = 2S
c. AB = 2S, AC = S√3, BC = S
d. AB = S√3, AC = 2S, BC = S

Answer 1

To construct a 30, 60, 90-degree triangle with the short leg (AB) equal to S, the sides are in the ratio 1:√3:2. Thus, correct dimensions are AB = S, AC = 2S, and BC = √3S, as identified in option a.

Step-by-step explanation:

To construct a 30, 60, 90-degree triangle with the short leg equal to AB, let's use the Pythagorean theorem and the special ratios that define the lengths of the sides of such a triangle. The sides are in the ratio 1:√3:2. Therefore, if AB = S (the short leg), then the hypotenuse (AC) is twice the length of AB, AC = 2S, and the longer leg (BC) is √3 times the length of AB, BC = √3S.

Option a represents this correctly: AB = S, AC = 2S, BC = √3S. The Pythagorean theorem confirms this with the equation a² + b² = c², which can be rewritten to solve for c: c = √(a² + b²).