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Two microphones are located 100 meters apart and each is 130 meters

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Two microphones are located 100 meters apart and each is 130 meters [#permalink]

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New post 03 Aug 2017, 08:51
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Two microphones are located 100 meters apart and each is 130 meters from the same listening station. If a transmitter is located half-way between the two microphones, what is the distance, in meters, between the transmitter and the listening station?

(A) 120
(B) 124
(C) 125
(D) 128
(E) 130

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Re: Two microphones are located 100 meters apart and each is 130 meters [#permalink]

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New post 03 Aug 2017, 09:06
Answer is A

You can draw an isosceles triangle with the base formed using two microphones (100 m) and the other two sides as 130 m (top vertex is the listening station)
transmitter is in the middle of base.

So applying pythagoras,
5,12,13 triangle

distance is 120
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Two microphones are located 100 meters apart and each is 130 meters [#permalink]

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New post 03 Aug 2017, 09:58
Since the microphones are located 100 m apart and
the transmitter is located halfway between the microphones,
distance between the microphone and the transmitter is 50m.

The microphone is around 130 meters from the listening station.
Since we are asked the distance between the listening station and the
transmitter, let that distance be x.

Apply Pythagoras theorem to the right angled triangle
formed between the microphone, the transmitter and the listening station

\(x^2 + 50^2 = 130^2\)
\(x^2 = 16900 - 2500\)
\(x^2 = 14400\)
\(x = 120\) (Option A)
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Two microphones are located 100 meters apart and each is 130 meters   [#permalink] 03 Aug 2017, 09:58
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