Given a right triangle with one acute angle measuring $60°$, how many distinct triangles (up to similarity) can be formed?

• A. $2$
• B. $3$
• C. $1$
• D. $0$

Answer: (C)

Verified step by step guidance

1. Identify the given information: the triangle is a right triangle, and one of its acute angles measures 60 degrees.
2. Recall that in a right triangle, the sum of the two acute angles must be 90 degrees because the right angle is 90 degrees and the total sum of angles in any triangle is 180 degrees.
3. Calculate the other acute angle by subtracting the given angle from 90 degrees: \$90^\circ - 60^\circ = 30^\circ$.
4. Recognize that the triangle's angles are now fixed as 90°, 60°, and 30°, which means the triangle's shape is uniquely determined up to similarity (all triangles with these angles are similar).
5. Conclude that only one distinct triangle (up to similarity) can be formed with these angle measures.