In the given figure ABCis a right triangle and right angled atB such t

1.	In the given figure ABCis a right triangle and right angled atB such that LBCA-2ZBAC.Show that hypotenuse AC-2BC.(Hint : Produce CB to a point D that BC = BD)
Answer» Triangle ABC is a right angled triangle at angle B .......givenAngle B=90degreeslet angle BAC=x degreesthen angle BCA=2x degreesthus, angle B+ angle BAC+ angle BCA= 180degrees .........sum of angles of triangle 90+x+2x=18090+3x=1803x=180-903x=90dividing both sides by 3x=30thenangle BAC=30degrees and angle BCA=2(30)=60degrees therefore the measures of angles of triangle ABC are 30,60 and 90 degrees here side AC is a hypotenusethereforein 30-60-90 triangle side opposite to 30degrees is half the hypotenusehere the side opposite to 30 degrees is side BC thereforeBC=1/2*ACthus 2BC=ACthusAC=2BC

In the given figure ABCis a right triangle and right angled atB such that LBCA-2ZBAC.Show that hypotenuse AC-2BC.(Hint : Produce CB to a point D that BC = BD)

Answer»

Triangle ABC is a right angled triangle at angle B .......givenAngle B=90degreeslet angle BAC=x degreesthen angle BCA=2x degreesthus,

angle B+ angle BAC+ angle BCA= 180degrees .........sum of angles of triangle

90+x+2x=18090+3x=1803x=180-903x=90dividing both sides by 3x=30thenangle BAC=30degrees and angle BCA=2(30)=60degrees

therefore the measures of angles of triangle ABC are 30,60 and 90 degrees

here side AC is a hypotenusethereforein 30-60-90 triangle

side opposite to 30degrees is half the hypotenusehere the side opposite to 30 degrees is side BC

thereforeBC=1/2*ACthus

2BC=ACthusAC=2BC