InterviewSolution
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InterviewSolution
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5.If tansit -mandt26. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squaresof the other two sides. Using the above, find the length of an altitude of an equilateraltriangle of side 2 cmchadow when the angle of |
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Answer» Given: A right angled ∆ABC, right angled at B To Prove- AC²=AB²+BC² Construction: draw perpendicular BD onto the side AC . Proof: We know that if a perpendicular is drawn from the vertex of a right angle of a right angled triangle to the hypotenuse, than triangles on both sides of the perpendicular are similar to the whole triangle and to each other. We have △ADB∼△ABC. (by AA similarity) Therefore, AD/ AB=AB/AC (In similar Triangles corresponding sides are proportional) AB²=AD×AC……..(1) Also, △BDC∼△ABC Therefore, CD/BC=BC/AC(in similar Triangles corresponding sides are proportional) Or, BC²=CD×AC……..(2) Adding the equations (1) and (2) we get, AB²+BC²=AD×AC+CD×AC AB²+BC²=AC(AD+CD) ( From the figure AD + CD = AC) AB²+BC²=AC . AC Therefore, AC²=AB²+BC² This theroem is known as Pythagoras theroem what is it's answer please tell |
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