Which of the following is a type of special right triangle commonly studied in trigonometry?

• A. A $45°$-$45°$-$90°$ triangle
• B. An equilateral triangle
• C. An isosceles triangle with all angles $60°$
• D. A scalene triangle

Answer: (A)

Verified step by step guidance

1. Understand that special right triangles are specific triangles with angle measures and side ratios that are commonly used in trigonometry for simplifying calculations.
2. Recognize that a 45\textdegree-45\textdegree-90\textdegree triangle is a special right triangle where the two legs are congruent, and the hypotenuse is \( \sqrt{2} \) times the length of each leg.
3. Note that an equilateral triangle has all sides equal and all angles equal to 60\textdegree, but it is not a right triangle and thus not classified as a special right triangle in trigonometry.
4. Identify that an isosceles triangle with all angles 60\textdegree is actually an equilateral triangle, which again is not a right triangle and not considered a special right triangle.
5. Understand that a scalene triangle has all sides and angles different, so it does not fit the criteria of special right triangles, which have specific angle measures and side ratios.