Multiple Choice
An equilateral triangle has sides of length . What is the length of its altitude?
71
views
2. Trigonometric Functions on Right Triangles
Special Right Triangles
Multiple Choice
Which of the following sets of side lengths could represent the side lengths of a -- triangle?
A
, ,
B
, ,
C
, ,
D
, ,
Verified step by step guidance1
Recall the side length ratios for a 30°-60°-90° triangle: the sides are in the ratio \(1 : \sqrt{3} : 2\), where the side opposite 30° is the shortest, the side opposite 60° is \(\sqrt{3}\) times the shortest side, and the hypotenuse (opposite 90°) is twice the shortest side.
For each given set of side lengths, identify the shortest side, the side that should correspond to \(\sqrt{3}\) times the shortest side, and the longest side (hypotenuse).
Check if the middle side is approximately \(\sqrt{3}\) times the shortest side by verifying if \(\text{middle side} = \text{shortest side} \times \sqrt{3}\) holds true.
Check if the longest side is twice the shortest side by verifying if \(\text{longest side} = 2 \times \text{shortest side}\) holds true.
The set of side lengths that satisfies both conditions correctly represents the sides of a 30°-60°-90° triangle.
Related Videos
Related Practice
