Question

In the right △abc m∠c=90°, bl is an angle bisector of ∠abc. What is the ratio cl:ac, if m∠bac=30°?

Answer 1

1/3

Explanation:

Answer 2

The ratio is
`(CL)/(AC)=(2BC)/(3AB)`

Explanation:

we know that

In the right triangle ABC

`cos(30\°)=AC/AB`

`AC=cos(30\°)(AB)`

we know that

`cos(30\°)=(√(3))/(2)`

substitute

`AC=(√(3))/(2)(AB)`

In the right triangle LBC

`tan(30\°)=CL/BC`

`CL=tan(30\°)(BC)`

we know that

`tan(30\°)=(√(3))/(3)`

substitute

`CL=(√(3))/(3)(BC)`

see the attached figure to better understand the problem

Find the ratio CL: AC

we have

`CL=(√(3))/(3)(BC)`

`AC=(√(3))/(2)(AB)`

`(CL)/(AC)=((√(3))/(3)(BC))/((√(3))/(2)(AB))=(2BC)/(3AB)`