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Kazeer [188]
2 years ago
11

What is the trigonometric ratio for sin Z?

Mathematics
1 answer:
Snowcat [4.5K]2 years ago
4 0

Answer:

\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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