We are given that $\angle Q$ is an acute angle with $\sin Q = 0.91$. We need to find the measure of $\angle Q$ to the nearest tenth of a degree.

1. Problem Description

We are given that $\angle Q$ is an acute angle with $\sin Q = 0.91$. We need to find the measure of $\angle Q$ to the nearest tenth of a degree.

2. Solution Steps

To find the measure of angle $Q$, we need to find the inverse sine (also known as arcsin) of 0.

9

1. $Q = \arcsin(0.91)$

Using a calculator, we find that

$Q \approx 65.5060144$ degrees.

We are asked to round to the nearest tenth of a degree. The hundredths place is 0, so we round down.

3. Final Answer

$m\angle Q \approx 65.5^{\circ}$