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

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Math Expert
Joined: 02 Sep 2009
Posts: 50711
A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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07 Feb 2016, 09:27
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Difficulty:

35% (medium)

Question Stats:

71% (01:53) correct 29% (01:49) wrong based on 125 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 [ 3.76 KiB | Viewed 1426 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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08 Feb 2016, 09:27
40√3
using tan 30=x/120
Manager
Joined: 09 Jul 2013
Posts: 109
Re: A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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08 Feb 2016, 09:34
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 $$\frac{120}{\sqrt{3}}= \frac{3*40}{\sqrt{3}}=40\sqrt{3}$$

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Dave de Koos

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Joined: 22 May 2016
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A boat leaves point A heading directly across the river to point P, 12  [#permalink]

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28 Jul 2018, 12:06
Bunuel wrote:

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

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

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