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What is the trigonometric ratio for sin Z?

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$$\large { \purple{ \sf {The \: value \: of \: sin \: Z \: is} \sf \frac{3}{5} }}$$

Step-by-step explanation:

$$\large{\underline{\underline{\pink{\sf{To \: \: find :-}}}}}$$

$$\textsf{The value of Sin Z}$$

$$\large{\red{\underline{\textsf{Given :-}}}}$$

YZ (B) = 32 (which the base of the triangle)

XZ (H) = 40 (which is the hypotenuse of the triangle)

$$\textsf{ \huge { \underline{ \orange{Solution :-}}}}$$

$$\sf{The \: formula \: to \: find} \sin Z = \frac{P}{H} \\ \textsf{which \: means} \\ \sf \rightarrow \frac{perpendicular}{hypotenuse}$$

But here we don't have perpendicular so we use Pythagoras theorem to find perpendicular

$${ \sf {(perpendicular)}^{2} + \sf{(base)}^{2} = \sf {(hypotenuse)}^{2} } \\ \sf {(P)}^{2} + \sf {(B)}^{2} = \sf {(H)}^{2}$$

let here P = P

$$\sf {(P)}^{2} + {(32)}^{2} = {(40)}^{2} \\ \sf {P}^{2} + 1024 = 1600 \\ \sf {P}^{2} = 1600 - 1024 \\ \sf {P}^{2} = 576 \\ \sf P = \sqrt{576} \\ \sf P = 24$$

Now we to find Sin ZPH

$$\sf \ \sin Z = \frac{P}{H} \\ \implies \frac{24}{40} \\ \implies \frac{6}{10} \\ \implies \frac{3}{5}$$
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