Given a right triangle where one of the acute angles $x$ has a measure of $51°$, how many distinct triangles (up to similarity) can be formed?

• A. $3$
• B. $0$
• C. $1$
• D. $2$

Answer: (C)

Verified step by step guidance

1. Recall that in a right triangle, one angle is always 90°.
2. Since one acute angle is given as \$51^\circ\(, the other acute angle must be \)90^\circ - 51^\circ = 39^\circ\( because the sum of angles in a triangle is \)180^\circ$.
3. Triangles are considered similar if their corresponding angles are equal, regardless of side lengths.
4. Given the angles \$51^\circ\(, \)39^\circ\(, and \)90^\circ$, any triangle with these angles will be similar to each other.
5. Therefore, only one distinct triangle (up to similarity) can be formed with an acute angle of \$51^\circ$ in a right triangle.