Saved Bookmarks
| 1. |
in a right angle triangle with side A and B and the hypotenuse c the altitude drawn from the hypotenuse is X prove that one upon a square + 1 upon B square equal to one upon x square |
|
Answer» Consider ∆ABC in which angle ABC=90°,AB=a,BC=b and AC=c.Let AM=x be altidude of AC from B.Take angle BAC=θ,angleBCA=90-θ.sinθ=x/a and sin(90-θ)=x/b=cosθusing (sinθ)^2+(cosθ)^2=1 we getx^2/a^2=1-x^2/b^2=>x^2(1/a^2+1/b^2)=1=>x^2=(a^2b^2)/(a^2+b^2) = (a^2b^2)/c^2 =>x=(ab)/c. |
|