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Math Help - trigonometry

  1. #1
    Member helloying's Avatar
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    trigonometry

    pls see the attactment
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  2. #2
    o_O
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    Since TA and TB are tangent to the circle, then extending the radius to the point of tangency will form right angles with them, i.e. \angle OAT = \angle OBT = 90^{\circ}

    Now, looking at \triangle TAB, we know it is isosceles since TA = TB. This implies \angle TAB = \angle TBA. Using the fact that the angles of a triangle add up to 180^{\circ}, you can deduce that \angle TAB = \angle TBA = 69^{\circ}

    But: \begin{aligned}\angle OAB & = \angle OAT - \angle TAB = 90^{\circ} - 69^{\circ} = 21^{\circ}\\ \angle OBA & = \angle OBT - \angle TBA = 90^{\circ} - 69^{\circ} = 21^{\circ} \end{aligned}

    So we have all the required angles to find AB and TA. To find AB, use the sine law for \triangle OAB. Then to find TA, use the sine law again for \triangle TAB (you'll need AB first).
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