Question

Given: ∆ABC, m∠C = 90° m∠ABC = 30° AL -∠ bisector, CL = 6 ft Find: LB

Answer 1

Answer: LB=12ft

Explanation:

CL=6ft, <ABC=30 degrees

<A = bisector, so <CAL = 30 degrees

AL = 12ft, leg opposite 30 degrees

<LAB = <ABL = 30 degrees

Triangle ALB = isosoles Triangle

LB=12ft

Answer 2

The length of BL is approximately 22.36 feet.

Given that ∆ABC is a right triangle with ∠ABC = 30° and ∠ACB = 60°, we can use the special right triangle ratios to find the lengths of the sides and the measures of the angles.

Since ∠ABC = 30°, we know that the opposite side (AC) is half the length of the hypotenuse (AB).

We are given that AL is the angle bisector of ∠BAC, so ∠BAL = ∠BAC/2 = 30°/2 = 15°.

Using the tangent function, we can find the length of CL:

tan(15°) = CL/BL

0.2679 = 6/BL

BL ≈ 22.36 ft

Therefore, the length of BL is approximately 22.36 feet.