Given: △ABC, m∠C=90° m∠ABC=30°, AL ∠ bisector LB=18m. Find: CL
1 answer:
Answer:
9 m
Step-by-step explanation:
∠CAB = 90° -∠ABC = 90° -30° = 60°
Since AL bisects angle A, we have ...
∠LAC = ∠LAB = 60°/2 = 30°
Then ∠BAL = ∠ABL = 30° and ΔABL is isosceles with AL = LB = 18 m.
The 30°-60°-90° triangle ALC has sides in the ratio ...
CL : CA : AL = 1 : √3 : 2
so
CL/AL = 1/2
CL = AL/2 = (18 m)/2 = 9 m
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It can help to draw a diagram
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