Question

Find the values of the sine, cosine, and tangent for ZA.

(TOP OF TRIANGLE IS (A))

Answer 1

`\bigstar\:{\underline{\sf{In\:right\:angled\:triangle\:ABC\::}}}\\\\`

• AC = 7 m
• BC = 4 m

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`\bf{\dag}\:{\underline{\frak{By\:using\:Pythagoras\: Theorem,}}}\\\\`

`\star\:{\underline{\boxed{\frak{\purple{(Hypotenus)^2 = (Perpendicular)^2 + (Base)^2}}}}}\\\\\\ :\implies\sf (AB)^2 = (AC)^2 + (BC)^2\\\\\\ :\implies\sf (AB)^2 = (AB)^2 = (7)^2 = (4)^2\\\\\\ :\implies\sf (AB)^2 = 49 + 16\\\\\\ :\implies\sf (AB)^2 = 65\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{AB = √(65)}}}}}\:\bigstar\\\\`

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☆ Now Let's find value of sin A, cos A and tan A,

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• sin A = Perpendicular/Hypotenus =
  `\sf (4)/(√(65)) * (√(65))/(√(65)) = \pink{(4 √(65))/(65)}`

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• cos A = Base/Hypotenus =
  `\sf (7)/(√(65)) * (√(65))/(√(65)) = \pink{(7 √(65))/(65)}`

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• tan A = Perpendicular/Base =
  `{\sf{\pink{(4)/(7)}}}`

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`\therefore\:{\underline{\sf{Hence,\: {\pmb{Option\:A)}}\:{\sf{is\:correct}}.}}}`