Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 23, 2024

Find the measure of $\angle X$ to the nearest degree if $\sin X = \frac{4}{9}$ .

STEP 1

Assumptions
1. The sine of angle $X$ is given as $\sin X = \frac{4}{9}$ .
2. We are looking for the measure of angle $X$ in degrees.
3. We assume that angle $X$ is in the range where sine is positive, which is between $0^\circ$ and $180^\circ$ .

STEP 2

To find the measure of angle $X$ , we will use the inverse sine function, which is denoted as $\sin^{-1}$ or arcsin. This function gives us the angle whose sine is a given number.
$X = \sin^{-1}\left(\frac{4}{9}\right)$

STEP 3

We will use a calculator to find the value of $X$ to the nearest degree. Make sure the calculator is set to degree mode.
$X \approx \sin^{-1}\left(\frac{4}{9}\right)$

STEP 4

Calculate the value of $X$ using the calculator.
$X \approx \sin^{-1}\left(\frac{4}{9}\right) \approx 26.4^\circ$

STEP 5

Round the value of $X$ to the nearest degree.
$X \approx 26^\circ$
The measure of $\angle X$ to the nearest degree is approximately $26^\circ$ .

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