Question

in a right angle triangle sin =5/13 find all the trigonometric ratios for the triangle​

Answer 1

Step-by-step explanation:

let angle be A so its given sinA=5/13

by Pythagoras theorem we get adjacent side as 12

cosA=12/13

tanA=5/12

secA=13/12

cosecA=13/5

cotA=12/5

Answer 2

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$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

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$\sf{\underline{\green{Given:-}}}$

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• In a right angle triangle $\sf{Sin\theta = \dfrac{5}{13}}$.

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$\sf{\underline{\green{Find:-}}}$

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• Find all the trigonometric ratios for the the triangle = ?

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$\sf{\underline{\green{Explanation:-}}}$

• Hypotenuse = 5
• Perpendicular = 13

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$\sf{\underline\purple{By\: Pythagoras\: theorem:-}}$

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$\bigstar\boxed{\sf{\red{(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2}}}$

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$\sf{\underline{\pink{Putting\:the\:values:-}}}$

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$\longrightarrow \sf {(13)^2 = (5)^2 + (b)^2}$

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$\longrightarrow \sf {169 = 25 + b^2}$

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$\longrightarrow \sf {169 - 25 = b^2}$

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$\longrightarrow \sf {144 = b^2}$

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$\longrightarrow{\gray{ \underbrace{\boxed{\underline{\underline{\blue{ \tt Base = 12 }}}}}}}$

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$\:\:\:\:\dag\bf{\underline{\underline \red{Hence:-}}}$

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$\:\:\footnotesize\bold{\underline{\underline{\sf{\red{The\: trigonometric \:ratios\: for \:the\: triangle \::-}}}}}$

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$\bigstar{\underline{\boxed{\sf\purple{Sin\theta = \dfrac{Perpendicular}{Hypotenuse}}}}}$

$\longrightarrow \sf {Sin\theta = \dfrac{5}{13} }$

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$\bigstar{\underline{\boxed{\sf\purple{Cos\theta = \dfrac{Base}{Hypotenuse}}}}}$

$\longrightarrow \sf {Cos\theta = \dfrac{12}{13} }$

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$\bigstar{\underline{\boxed{\sf\purple{Tan\theta = \dfrac{Perpendicular}{Base}}}}}$

$\longrightarrow \sf {Sin\theta = \dfrac{5}{12} }$

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$\bigstar{\underline{\boxed{\sf\purple{Cot\theta = \dfrac{Base}{Perpendicular}}}}}$

$\longrightarrow \sf {Cot\theta = \dfrac{12}{5} }$

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$\bigstar{\underline{\boxed{\sf\purple{Sec\theta = \dfrac{Hypotenuse}{Base}}}}}$

$\longrightarrow \sf {Sin\theta = \dfrac{13}{12} }$

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$\bigstar{\underline{\boxed{\sf\purple{Cosec\theta = \dfrac{Hypotenuse}{Perpendicular}}}}}$

$\longrightarrow \sf {Cosec\theta = \dfrac{13}{5} }$

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$\rule{200}{2}$