Question

In triangle ABC is a right angle at B such that angleBCA=angle2BCA .show that AC=2BC

Answer 1

Triangle ABC is a right angled triangle at angle B .......given

Angle B=90degrees

let angle BAC=x degrees

then angle BCA=2x degrees

thus,

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

90+x+2x=180

90+3x=180

3x=180-90

3x=90

dividing both sides by 3

x=30

then

angle 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 hypotenuse

therefore

in 30-60-90 triangle

side opposite to 30degrees is half the hypotenuse

here the side opposite to 30 degrees is side BC

therefore

BC=1/2*AC

thus

2BC=AC

thus

AC=2BC

please forgive if there are mistakes

Answer 2

Answer:

wrong question,, , , , , ,, ,,,,,