Question : In $\triangle X Y Z, \angle X=90^{\circ}, YZ=15 \mathrm{~cm}$, and $X Z=12 \mathrm{~cm}$. Then find $\cos Y$.
Option 1: $\frac{2}{5}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{3}{5}$
Option 4: $\frac{3}{4}$
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Correct Answer: $\frac{3}{5}$
Solution :
$\cos Y = \frac{\text{Base}}{\text{Hypotenuse}}$
Applying Pythagoras theorem, we get,
$\small{\text{Hypotenuse}}^2 = \text{Base}^2 + \text{Perpendicular}^2$
⇒ $15^2=b^2 + 12^2$ [Let $b$ be the length of the base of the triangle]
⇒ $b^2 = 81$
⇒ $b=9$ cm
$\therefore\cos Y = \frac{9}{15}= \frac{3}{5}$
Hence, the correct answer is $\frac{3}{5}$.
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