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A boat leaves point A heading directly across the river to point P, 12

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A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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New post 07 Feb 2016, 10:27
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Question Stats:

72% (01:18) correct 28% (01:23) wrong based on 102 sessions

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A boat leaves point A heading directly across the river to point P, 120 yards away. A swift current immediately changes the boat’s direction, causing it to land instead at point B. How many yards is point B from the intended destination, P?

A. 40
B. 45
C. 60
D. \(40 \sqrt{3}\)
E. \(60 \sqrt{3}\)

Attachment:
2016-02-07_2125.png
2016-02-07_2125.png [ 3.76 KiB | Viewed 1174 times ]

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Re: A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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New post 08 Feb 2016, 10:27
40√3
using tan 30=x/120
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Re: A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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New post 08 Feb 2016, 10:34
We are shown a 30-60-90 triangle and given the length of the long side = 120.
The ratio of the long side to the short side is \(\sqrt{3}:1\), therefore the length of the short side, PB is \(\frac{120}{\sqrt{3}}= \frac{3*40}{\sqrt{3}}=40\sqrt{3}\)

Answer: D
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A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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New post 28 Jul 2018, 13:06
Bunuel wrote:
Image
A boat leaves point A heading directly across the river to point P, 120 yards away. A swift current immediately changes the boat’s direction, causing it to land instead at point B. How many yards is point B from the intended destination, P?

A. 40
B. 45
C. 60
D. \(40 \sqrt{3}\)
E. \(60 \sqrt{3}\)

Attachment:
2016-02-07_2125.png

∆ APB is a 30-60-90 special triangle
Vertex P = 90°, vertex A = 30°
Vertex B must = 60° (180° in a triangle)
We have a 30-60-90 triangle

Sides opposite those angles, respectively, are in ratio \(x: x\sqrt{3}: 2x\)

Length of BP, opposite the 30° angle = \(x\)

Side AP = 120 and is opposite the 60° angle
Length of 120 thus corresponds with \(x\sqrt{3}\)
Set them equal, solve for \(x\)
\(120=x\sqrt{3}\)
\(x=\frac{120}{\sqrt{3}}\)
\(x=(\frac{120}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}})=\frac{120\sqrt{3}}{3}=40\sqrt{3}\)


Point B is \(40\sqrt{3}\) yards from P

Answer D
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A boat leaves point A heading directly across the river to point P, 12 &nbs [#permalink] 28 Jul 2018, 13:06
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