Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 months ago

A diagram shows a circle centre o,radius 9cm.The tangent to the circle at A meets OB produced at T.The area of the sector OAB is 24cm^2. ?

Calculate the area of the triangle OAT..

Helppppppp pleasssssss

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  • 4 months ago
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    Area of a sector of radius r and angle θ

               Area = ½r²θ

                   24 = ½(9)²θ

              ∴ θ = 16/27

    ━━━━━━━━━━━━

    Tangent ratio

    tanθ = ( AT ) / ( OA )

    ∴ AT = ( OA ) tanθ

        AT = 9 tan(16/27)

    ━━━━━━━━━

    Area of Triangle OAT

    Area = ½ ( OA )( AT )

              = ½ ( 9 )9 tan(16/27) 

              = 27.27 cm²

    ━━━━━━━━━

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