In the given diagram,both ABC and DBE are right triangles,B being the right angle for both.They have hypotenuses of same length where F is the midpoint for both.DE is perpendicular on BC.If,the area of ABC is √3 times of DEB,Find ∠BDE.
[figure not drawn to scale]
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According to the question, 2 1 sinθ.2x.y= 2 √ 3 .y.x
thus, sinθ= 2 √ 3 =sin60°. So,θ=∠ACB=60°
NOW ∠AFD=30°. from the picture, ▲AFD is an isosceles.so,∠ADF= 2 1 8 0 − 3 0 °=75°
we also know, ∠ADB=60° [because,∠ADB=∠ACB as the both lie on the same chord]
Finally, ∠BDE=∠ADF-∠ADB=75°-60°=15°
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