Question

What is the trigonometric ratio for sin Z?

Enter your answer, as a simplified fraction, in the boxes.

Answer 1

`\large { \purple{ \sf {The \: value \: of \: sin \: Z \: is} \sf (3)/(5) }}`

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 = (P)/(H) \\ \textsf{which \: means} \\ \sf \rightarrow (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 = √(576) \\ \sf P = 24`

Now we to find Sin ZPH

`\sf \ \sin Z = (P)/(H) \\ \implies (24)/(40) \\ \implies (6)/(10) \\ \implies (3)/(5)`