Question

In right triangle ABC, where angle C is 90 degrees, the angle bisector of angle ABC is BL. If angle BAC is 30 degrees, what is the ratio of CL to AC?

A) 1:1
B) 1:2
C) 2:1
D) 1:√3

Answer 1

The ratio of CL to AC in the given right triangle is 1:2.

Step-by-step explanation:

In right triangle ABC, angle C is 90 degrees, angle bisector of angle ABC is BL. If angle BAC is 30 degrees, we need to find the ratio of CL to AC.

Since angle C is 90 degrees and angle ABC is bisected, angle CBL and angle ABC are congruent, and angle BCL is half of angle ABC, which is 15 degrees.

Using the sine function, we can find the ratio of CL to AC as sin(15 degrees)/sin(30 degrees). Simplifying this expression gives us CL/AC = 1/2. Therefore, the ratio of CL to AC is 1:2 (option B).