91Ó°ÊÓ

If$\mathrm{θ}$is any angle in a given right angle triangle, then the trignometric ratio is given as,

$\sin \mathrm{θ}=\frac{\text{±ô±ð²Ô²µ³Ù³ó â¶Ä‰o´Ú â¶Ä‰s¾±»å±ð â¶Ä‰o±è±è´Ç²õ¾±³Ù±ð â¶Ä‰t´Ç â¶Ä‰}∠\mathrm{θ}\text{ â¶Ä‰â¶Ä‰}}{\text{±ô±ð²Ô²µ³Ù³ó â¶Ä‰o´Ú â¶Ä‰h²â±è´Ç³Ù±ð²Ô³Ü²õ±ð}}$

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.

$\begin{array}{l}\sin X=\frac{\text{±ô±ð²Ô²µ³Ù³ó â¶Ä‰o´Ú â¶Ä‰s¾±»å±ð â¶Ä‰o±è±è´Ç²õ¾±³Ù±ð â¶Ä‰t´Ç â¶Ä‰}∠X\text{ â¶Ä‰â¶Ä‰}}{\text{±ô±ð²Ô²µ³Ù³ó â¶Ä‰o´Ú â¶Ä‰h²â±è´Ç³Ù±ð²Ô³Ü²õ±ð}}\\ \sin X=\frac{\text{±ô±ð²Ô²µ³Ù³ó â¶Ä‰o´Ú â¶Ä‰Y´Ü}}{\text{±ô±ð²Ô²µ³Ù³ó â¶Ä‰o´Ú â¶Ä‰X´Ü}}\\ \sin X=\frac{9}{15}\\ \sin X=0.6\\ X={\sin }^{−1}\left(0.6\right)\\ X=36.87°\end{array}$

The measure of angle $X$is$36.87°$.

Here, role="math" localid="1647930486163" $36.87°≈37°\text{ â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â€‰â¶Ä‰â¶Ä‰â€‰â€‰}\left[\text{¸é´Ç³Ü²Ô»å¾±²Ô²µâ€‰â¶Ä‰t´Ç â¶Ä‰t³ó±ð â¶Ä‰n±ð²¹°ù±ð²õ³Ù â¶Ä‰d±ð²µ°ù±ð±ð}\right]$.

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