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
AND find the measurement of
Answers
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°
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Shane and abha earned a team budget that required their team to collect no less than 2000 cans for recycling. Abha collected 178 more cans than Shane did. Write an inequality to determine the number of cans , s, that Shane could have collected
Answers
Answer:
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Let
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Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling
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Step-by-step explanation:
Answer:
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Answers
The text of the question is not visible in the answering window. I'll reproduce it here:
BD bisects <ABC.
m <ABD= 2.5x + 8.6
m<CBD = 3.5x - 3.4
Find m<ABC
Answer:
[tex]m\angle ABC = 77.2^\circ[/tex]
Step-by-step explanation:
We have an angle ABC and a line BD bisecting it.
If an angle is bisected, then the two formed angles are congruent, that is
[tex]m\angle ABD=m\angle CBD[/tex]
Substituting the algebraic expressions for both angles:
[tex]2.5x + 8.6=3.5x - 3.4[/tex]
Subtracting 8.6 and 3.5x:
[tex]2.5x - 3.5x = -8.6 - 3.4[/tex]
Operating:
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[tex]x = 12[/tex]
The two angles are:
[tex]m\angle ABD=2.5x + 8.6=2.5(12) + 8.6=38.6^\circ[/tex]
[tex]m\angle CBD=3.5x - 3.4 = 38.6^\circ[/tex]
As expected, both angles have the same measure.
The measure of the total angle ABC is twice any of those:
[tex]m\angle ABC = 2*38.6^\circ=77.2^\circ[/tex]
[tex]\mathbf{m\angle ABC = 77.2^\circ}[/tex]
