SAT Math: In a 30-60-90 Right Triangle with Hypotenuse 14, Find the Longer Leg

Exact Question Text

In a right triangle with angles 30, 60, and 90 degrees, the hypotenuse has length 14. What is the length of the side opposite the 60-degree angle?

1. Step-by-Step Formal Solution

1. 30-60-90 ratio is x : x*sqrt(3) : 2x.
2. 2x = 14 => x = 7.
3. Longer leg = 7*sqrt(3) ~= 12.124.

2. Fast Desmos / Calculator Shortcut

Evaluate 7 * sqrt(3) in Desmos.

3. Distractor Trap Analysis

• Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
• Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
• Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
• Option Correct: Accurately satisfies all algebraic and logical constraints.