Question

the measure of one of the acute angles in a right triangle is $56\frac{2}{3}$. what is the measure of the other acute angle? write your answer as a decimal rounded to the nearest hundredth.

Explanation:

Step1: Convert the mixed number to a decimal

We know that \(56\frac{2}{3}=56 + \frac{2}{3}\). Since \(\frac{2}{3}\approx0.67\), then \(56\frac{2}{3}\approx56.67\).

Step2: Use the angle - sum property of a triangle

In a right - triangle, the sum of the interior angles is \(180^{\circ}\), and one angle is \(90^{\circ}\). Let the two acute angles be \(A\) and \(B\). We know that \(A + B+90^{\circ}=180^{\circ}\), so \(A + B=90^{\circ}\).
If one acute angle \(A = 56\frac{2}{3}\approx56.67^{\circ}\), then the other acute angle \(B=90 - 56.67\).
\(B = 33.33^{\circ}\)

Answer:

\(33.33\)