Given:
In triangle [tex]XYZ,m\angle X=90^\circ, m\angle Y=45^\circ, m\angle Z=45^\circ, XZ=y,YZ=15\sqrt{2}[/tex].
To find:
The value of y.
Solution:
In a right angle triangle,
[tex]\sin \theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
Using the above ratio for the triangle XYZ, we get
[tex]\sin Y =\dfrac{XZ}{YZ}[/tex]
[tex]\sin 45^\circ =\dfrac{y}{15\sqrt{2}}[/tex]
[tex]\dfrac{1}{\sqrt{2}}=\dfrac{y}{15\sqrt{2}}[/tex]
[tex]\dfrac{15\sqrt{2}}{\sqrt{2}}=y[/tex]
[tex]15=y[/tex]
Therefore, the correct option is C.
