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# Help sorry for the bother

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What is the value of y in the diagram below A.7 square root 2

B.2 square root 3

C.square root 14

D.square root 5

Jul 25, 2019

#1
+3 m∠ABD  =  m∠CBA  because they are the same angle

m∠BDA  =  m∠BAC  because they are both right angles.

So by the AA similarity theorem, triangle ABD is similar to triangle CBA

Do you see what to do next?

Jul 25, 2019
#2
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no i thought i did but then i got square root of 10 so no i don't get it still

sorry can you explain it further plz

Guest Jul 25, 2019
#5
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Let's just look at the similarity statement  △ABD ~ △CBA

ABD ~ △CBA     AB  in the first triangle corresponds to  CB  in the second triangle.

△ABD ~ △CBA     BD  in the first triangle corresponds to  BA  in the second triangle.

So:

AB / CB  =  BD / BA

Do you see where that came from?

All that's left to do is plug in the lengths of those sides and solve for  y .

hectictar  Jul 25, 2019
#6
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wait it is square root 14 right i just got that

Guest Jul 25, 2019
#7
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Yep! That's what I got too hectictar  Jul 26, 2019
#3
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(5 +2) / y = y/2

7 / y = y / 2      cross myltiply

y^2 = 14

y = sqrt(14)

Jul 25, 2019
#4
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are yousure thats right or is 7 square root 2

Guest Jul 25, 2019
#8
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sqrt (14) is not 7root 2

sqrt(98)= sqrt(49)*sqrt(2) = 7sqrt2

Jul 26, 2019
#9
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Tan ABC = y / (5+2) = Tan DBA = 2 / y
Or: y / 7 = 2 / y      Cross multiply
y^2 = 14
y = Sqrt(14)

Jul 26, 2019