Mathematics High School

In the right ∆ABC, BL is an angle bisector. If LB = 1.2 in and LC = 0.6 in. Find:

- The distance from L to AB.

- m∠ABC

In The Right ABC, BL Is An Angle Bisector. If LB = 1.2 In And LC = 0.6 In. Find: - The Distance From

Answers

Answer 1

Answer:

Distance of L from AB = 0.6 in.

m∠ABC = 60°

Step-by-step explanation:

Given:

LB = 1.2 in

LC = 0.6 in

We have to find the distance of point L to AB or length of LD.

From right triangle ΔBCL,

Sin(∠LBC) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

                 = [tex]\frac{LC}{LB}[/tex]

                 = [tex]\frac{0.6}{1.2}[/tex]

                 = [tex]\frac{1}{2}[/tex]

m∠LBC = 30° [Since ∠LBC is an acute angle]

Since, ∠LBC ≅ ∠LBA

m∠LBA = 30°

Now from right triangle ΔLDC,

sin(∠LBA) = [tex]\frac{LD}{BL}[/tex]

sin(30)° = [tex]\frac{LD}{1.2}[/tex]

[tex]\frac{1}{2}=\frac{LD}{1.2}[/tex]

LD = 0.6

Therefore, Distance of point L from AB is 0.6 in.

m∠ABC = m∠ABL + m∠LBC

             = 30° + 30°

             = 60°

In The Right ABC, BL Is An Angle Bisector. If LB = 1.2 In And LC = 0.6 In. Find: - The Distance From

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