Given a right triangle where angle $y$ is larger than angle $x$, what is the approximate value of $y-x$ if $y$ and $x$ are two of the triangle's angles? Choose the closest value.

• A. $17.2°$
• B. $4.9°$
• C. $11.1°$
• D. $6.2°$

Answer: (C)

Verified step by step guidance

1. Recall that in any triangle, the sum of the interior angles is always \(180^\circ\). For a right triangle, one angle is \(90^\circ\), so the other two angles, \(x\) and \(y\), must satisfy the equation \(x + y = 90^\circ\).
2. Since \(y\) is larger than \(x\), we know that \(y > x\) and both are acute angles (less than \(90^\circ\)).
3. Express the difference \(y - x\) in terms of \(x\) and \(y\). Using the sum \(x + y = 90^\circ\), rewrite \(y\) as \(90^\circ - x\).
4. Substitute \(y = 90^\circ - x\) into the difference \(y - x\) to get \(y - x = (90^\circ - x) - x = 90^\circ - 2x\).
5. To find the approximate value of \(y - x\), you would need the value of \(x\) or \(y\). Since the problem provides multiple-choice options and the correct answer is \(11.1^\circ\), this suggests that \(x\) is approximately \(39.45^\circ\) (because \(90^\circ - 2 \times 39.45^\circ = 11.1^\circ\)).