SOLUTION: 2 vertical telephone poles are 50 ft apart. One is 20 ft tall while the other is 60 ft tall. A blue laser shines from the top of shorter pole to the base of the taller pole and a r

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Question 676670: 2 vertical telephone poles are 50 ft apart. One is 20 ft tall while the other is 60 ft tall. A blue laser shines from the top of shorter pole to the base of the taller pole and a red laser shines from the top of the taller pole to the base base of the shorter pole. What is the height of the point where the laser beams meet?
a) 15 ft
b) 18 ft
c) 20 ft
d) 21 ft
e) None of the above
Found 2 solutions by Alan3354, partha_ban:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2 vertical telephone poles are 50 ft apart. One is 20 ft tall while the other is 60 ft tall. A blue laser shines from the top of shorter pole to the base of the taller pole and a red laser shines from the top of the taller pole to the base base of the shorter pole. What is the height of the point where the laser beams meet?
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The height of the point is similar to parallel resistors (strangely enough).
h = 20*60/(20+60)
h = 15 feet
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It can be done geometrically, but it's not necessary.

Answer by partha_ban(41) About Me  (Show Source):
You can put this solution on YOUR website!

Let PQ be the pole with height 20' and RS be the pole with height 60' and QR be the distance between them which is 50'. Two laser beams have crossed at T. We need to find the height TU.
Let us assume UR = x'.
Triangle PQR and TUR are similar since angle Q = angle U (each right angle), angle R is common and angle P = angle T.
Therefore, PQ%2FTU+=+QR%2FUR
20%2FTU+=+50%2Fx
20x+=+50%2ATU
x+=+50%2ATU%2F20
x+=+5%2ATU%2F2 ... ... ...(1)
Again triangle QRS and QUT are similar since angle R = angle U (each right angle), angle Q is common and angle S = angle T.
Therefore, SR%2FTU+=+QR%2FQU
60%2FTU+=+50%2F%2850-x%29
60%2A%2850-x%29+=+50%2ATU
%2860%2A%2850-x%29%29%2F10+=+%2850%2ATU%29%2F10
6%2A%2850-x%29+=+5%2ATU
300+-+6x+=+5%2ATU
300+-+5%2ATU+=+6x
6x+=+300+-+5%2ATU
x+=+%28300+-+5%2ATU%29%2F6 ... ... ...(2)
From (1) and (2),
5%2ATU%2F2+=+%28300-5%2ATU%29%2F6
5%2ATU%2A6+=+%28300-5%2ATU%29%2A2
30%2ATU+=+600-10%2ATU
30%2ATU+%2B+10%2ATU+=+600
40%2ATU+=+600
TU+=+600%2F40+=+15
Therefore the height of the point where the laser beams meet = 15'