Given: ∆ABC, m∠C = 90° m∠BAC = 2m∠ABC
BC = 24 cm,
AL
− ∠ bisector
Find: AL

16 units

Step-by-step explanation:

Given that in triangle ABC, m∠C=90,

it means m∠A +∠B= m∠BAC + m∠ABC = 90

m∠ABC = 90 - m∠BAC

Also given that;m∠BAC = 2m∠ABC

So,

m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC

m∠BAC +2m∠BAC = 180

3m∠BAC = 180

m∠BAC=180/3 = 60

m∠ABC = 60/3 = 30

thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,

AC=24/√3=8√3AL bisects angle A =>m∠LAC=30

ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16

$450 i think. hope this ☺

most likely linear (proportionate)

step-by-step explanation:

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