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Calculate the length of AC if BD=30cm,∆ABC=30° and ∆ADC=45° |
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Answer» -step explanation:Let LENGTH of AB=X cm.In right angled triangle ABD , AB/BD=tan 45°.or. x/BD = 1 => BD=x cm.BC= BD-CD = (x-30) cm.In right angled triangle ABC , AB/BC= tan60°or. x/(x-30) = √3.or. √3.x -30√3 = x.or. x(√3–1) = 30√3.or. x= 30.√3/(√3–1) = 30√3×(√3+1)/(√3–1).(√3+1).or. x =15√3(√3+1) = 15(3+√3) cm = 70.98 cm.Thus , length of AB= x = 70.98 cm.and length of BC= (x-30) = 40.98 cm. Answer. |
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