Question

Given: ∆ABC, m∠C = 90°

m∠ABC = 30°

AL
- ∠ bisector, CL = 6 ft
Find: LB

Answer:
LB =
ft

Answer 1

LB = 12ft

Explanation:

m< CAB = 60 because of the triangle sum theorem

We can use triangle sum theorem to find the measure of all the angles in triangle CLA.

m< CAL = 60/2 = 30, because AL is a angle bisector

The m<CLA = 60 because of the triangle sun theorem

Then we can use properties of a 30 - 60 - 90 triangle.

LA = 12

Then, we also know that m< ALC = 30 because that is what is reamining of that angle.

So, we can see that triangle ALB is a isosceles triangle.

Then LA would equal LB by the definition of a Isosceles triangle, so LB would be 12 as well.