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

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) (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?
-------------------
The height of the point is similar to parallel resistors (strangely enough).
h = 20*60/(20+60)
h = 15 feet
-------------------
It can be done geometrically, but it's not necessary.
Answer by partha_ban(41) (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,

... ... ...(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,

... ... ...(2)
From (1) and (2),

Therefore the height of the point where the laser beams meet = 15'
RELATED QUESTIONS
Two telephone poles, 30 ft and 39 ft high, respectively, are 60 ft apart. How long is the (answered by checkley77)
Two telephone poles, 30 ft and 39 ft high, respectively, are 60 ft apart. How long is the (answered by checkley77)
A wire is run between the tips of two poles. One pole is 23 ft. taller than the other... (answered by stanbon)
A wire is run between the tips of two poles. One pole is 23 ft taller than the other... (answered by ankor@dixie-net.com)
A 3.5 ft child cast a 60 in. shadow. She is standing next to a telehone pole that casts... (answered by solver91311)
a telephone pole is 60 ft tall. A guy wire 85 ft long is attached from the ground to the... (answered by fractalier)
The cable for a suspension bridge is shaped like a parabola. The towers are 100 ft tall... (answered by ankor@dixie-net.com)
Two vertical poles have heights 7 ft. and 12 ft. A rope is stretched from the top of each (answered by Alan3354,richwmiller)
A building casts a 200 ft long shadow. At the same time, your shadow is 5ft long. you are (answered by JBarnum)