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Anna71 [15]
3 years ago
6

Line L bisects and is perpendicular to AB and CD, AB =140, and LM=24. what is the length of NQ?

Mathematics
1 answer:
geniusboy [140]3 years ago
4 0

Answer:

if line L bisects and perpendicular to both segments AB and CD, we can conclude that AB //CD  

so AB = CD and AB // CD  

so what is M, where is it located. and N and Q, what are those?

Step-by-step explanation:


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∠EBA = 180° - 90° - 60° = 30°

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ΔEBA ≅ ΔDAC because of the AAA postulate

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sin ∠EAB = EB/AB       (sin 60°)   EB = (0.8660)AB

cos ∠EAB = EA/AB      (cos 60°)  EA = (0.5)AB

cos ∠DAC = AD/CA     (cos 30°)  AD = (0.8660)CA

sin ∠DAC = CD/CA      (sin 30°)   CD = (0.5)CA

ED = EA + AD

ED = (0.5)AB + (0.8660)CA

since AB = CA,  ED = 1.366CA

since EB = (0.8660)AB and AB = CA, then EB = 0.866CA

since CD = 0.5CA,

EB  + CD = 0.866CA + 0.5CA = 1.366CA

EB + CD = 1.366CA

1.366CA = 1.366CA

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