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 fraction to decimal

First, convert \(56\frac{2}{3}\) to a decimal. \(56\frac{2}{3}=56 + \frac{2}{3}\). Since \(\frac{2}{3}\approx0.67\), then \(56\frac{2}{3}\approx56.67\).

Step2: Use the angle - sum property of a right - triangle

In a right - triangle, the sum of the two acute angles is \(90^{\circ}\). Let the measure of the unknown acute angle be \(x\). Then \(x + 56.67=90\).

Step3: Solve for \(x\)

Subtract \(56.67\) from both sides of the equation: \(x=90 - 56.67\).

Answer:

\(33.33\)