Answer:
[tex]\overline {LD}[/tex] = 0.6 inch
m∠ABC = 60°
Step-by-step explanation:
The given parameters are;
The given triangle ΔABC = A right triangle
The angle bisector of ∠CBA = BL
The length of BL = LB = 1.2 in.
The length of LC = 0.6 in.
We have;
[tex]\overline {LB}[/tex] ≅ [tex]\overline {LB}[/tex] reflexive property
∠ABC = ∠CBL + ∠DBL and ∠CBL ≅ ∠DBL definition of bisected angle
∠CBL = ∠DBL by definition of congruency
∠CLB + ∠CBL = ∠CLB + ∠DBL = 90°, opposite angles of a the right angle triangle are supplementary
∴ ∠CLB = ∠CLB by addition property of equality
ΔLDB ≅ ΔLBC are congruent by the Angle-Side-Angle rule of congruency
∴ [tex]\overline {LD}[/tex] ≅ [tex]\overline {LC}[/tex] Congruent Parts of Congruent Triangles are Congruent (CPCTC)
[tex]\overline {LD}[/tex] = [tex]\overline {LC}[/tex] = 0.6 in. by definition of congruency
[tex]\overline {LD}[/tex] = 0.6 in.
sin(m∠CBL) = Opposite side/(Hypotenuse side) = [tex]\overline {LC}[/tex]/[tex]\overline {LB}[/tex] = 0.6/1.6 = 1/2
m∠CBL = sin⁻¹(1/2) = 30°
m∠CBL = m∠DBL = 30°
m∠ABC = m∠CBL + m∠DBL = 30° + 30° = 60°
m∠ABC = 60°
