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°
