Question

question 7 of 10
a certain triangle has a 30° angle and a 60° angle. which must be a true statement about the triangle?
a. two sides of the triangle have the same length.
b. the second - longest side is twice as long as the shortest side.
c. the longest side is twice as long as the shortest side.
d. the longest side is √3 times as long as the shortest side.

Explanation:

Step1: Find third angle

Sum of angles: 180° - 30° - 60° = 90°, right triangle.

Step2: 30-60-90 side ratio

Sides: shortest (30°) : medium (60°) : longest (90°) = 1 : √3 : 2.

Step3: Evaluate options

A: No equal sides. B: Medium=√3×shortest≠2×shortest. C: Longest=2×shortest. D: Longest=2×shortest≠√3×shortest.

Answer:

C. The longest side is twice as long as the shortest side.