Question

Find $\mathit{m}\mathbf{\angle }\mathit{X}$to the nearest degree.

Short answer

Measure of angle $X$to the nearest degree is given as,

$\mathit{m}\mathbf{\angle }\mathit{X}\mathbf{=}\mathbf{37}\mathbf{°}$

Step-by-step solution

Step 1. Define the trigonometric ratio ‘sinθ’.

If$\theta$is any angle in a given right angle triangle, then the trignometric ratio is given as,

$\sin \theta =\frac{\text{length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}side\hspace{0.17em}\hspace{0.17em}opposite\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}\angle \theta }{\text{length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}hypotenuse}}$

Step 2. Calculate the measure of angle X (m∠X).

Observe the figure.

From the figure, $XZ$is hypotenuse (side opposite to 90 degree) and length of $XZ$is 15 units.

$YZ$is side opposite to angle $X$and the length of $YZ$is 9 units.

$\begin{array}{l}\sin X=\frac{\text{length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}side\hspace{0.17em}\hspace{0.17em}opposite\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}}\angle X}{\text{length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}hypotenuse}}\\ \sin X=\frac{\text{length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}YZ}}{\text{length\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}XZ}}\\ \sin X=\frac{9}{15}\\ \sin X=0.6\\ X={\sin }^{-1}\left(0.6\right)\\ X=36.87°\end{array}$

Step 3. State the conclusion.

The measure of angle $X$is$36.87°$.

Here, role="math" localid="1647930486163" $36.87°\approx 37°\left[\text{Rounding\hspace{0.17em}\hspace{0.17em}to\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}nearest\hspace{0.17em}\hspace{0.17em}degree}\right]$.

Therefore, measure of angle $X$$(m\angle X)$to the nearest degree is $37°$.