Or, if you don't want trigonometry, draw \(AD\) perpendicular to \(BC\) at \(D\). Since angles \(B\) and \(C\) both measure 75 degrees, you have no choice, but to use the ratio \(\frac{AD}{AB}=\frac{AD}{AC}=\frac{\sqrt{2}+\sqrt{6}}{4}\) which still comes from trigonometry.

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## Comments

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TopNewestUse the sine formula for the area of the triangle. \([ABC]=\frac{1}{2}(AB)(AC) \sin A\).

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by using this formula: Area=1/2(AB)(AC)sinA. area=1/2(10)(10)1/2=25 cm^2

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area=1/2

1010*sin30=25 cm^2Log in to reply

Using cosine law you will determine BC.After that using hero's formula you will determine the area of triangle

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25cm^2 as the formula is (1/2)(10)(10)(sin 30)=25 (sin 30 =1/2)

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Or, if you don't want trigonometry, draw \(AD\) perpendicular to \(BC\) at \(D\). Since angles \(B\) and \(C\) both measure 75 degrees, you have no choice, but to use the ratio \(\frac{AD}{AB}=\frac{AD}{AC}=\frac{\sqrt{2}+\sqrt{6}}{4}\) which still comes from trigonometry.

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