Question

ABC is a right triangle and right angled at B such that ∠BCA = 2∠BAC. 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 since it's my first answer on brainly

Answer 2

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