Direction sense

Geometry Level 1

A man walks 5 meters north from his house, turns left 9 0 90^\circ , walks 12 meters further and reaches a park. How far, in meters, is the park from his house?


The answer is 13.

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33 solutions

One can make use of the Pythagorean Theorem for right triangles.

Let the length of the side (of the triangle) be 5 5 meters and the length of the base (of the triangle) be 12 12 meters.

Required distance

= 1 2 2 + 5 2 =\sqrt{12^{2}+5^{2}}

= 169 = 13 =\sqrt{169}=\boxed{13} .

Christ, ask me a simple maths question, or at least a straightforward one, if you want to get cocky, let's start to talk about the English language

andrew cooper - 5 years, 10 months ago

Why make it so complicated?

andrew cooper - 5 years, 10 months ago

I think a lot of people instead of answering how far the park is from his house, are answering how far he walked to the park from his house and are assuming they're the same.

Genifer Genise - 5 years, 10 months ago
Lee Isaac
Jun 2, 2015

You didn't specify what units to express our answer in... I could say 1300 centimeters and it should also be correct.

Correct Lee Isaac.

andrew cooper - 5 years, 10 months ago

Its using meters as measurement so you would have to follow inn suit

Emily Holmes - 5 years, 10 months ago

I was going to say that 13 is wrong as well, it has to have units.

Chase Eric - 5 years, 10 months ago
Prakhar Dhumas
May 4, 2015

Robert Lucas
Oct 25, 2015

Doesn't everyone know their Pythagorean Triples? ;)

Yes, 3,4,5 5,12,13 :D

Muhamad Ramdan - 5 years, 4 months ago
Leonardo Fajardo
Sep 8, 2015

apply the PYTHAGOREAN theorem..

x=sqrt(12^2+5^2)

Deepak Gowda
Jun 21, 2014

Using Pythagoras theorem, square root of 12^2 + 5^2 gives 13

Where is the office? We didn't cm across any thing said abt office in the question... At first question is itself wrong

shree harry - 6 years, 11 months ago

the man walks to park from his house. where does the office come from???

आशुतोष सिंह - 6 years, 11 months ago

totally wrong question....:/

chaitragandha patil - 6 years, 11 months ago

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A perfect problem where a beginner can test his attentiveness and smartness.

Vijay Kumar - 5 years, 4 months ago

Then first please edit that thing and correct it kindly

Tajuddin Sayyad - 6 years, 11 months ago
Noel Cruz
Dec 28, 2016

It is displacement, not distance

Ajin Varghese
Dec 31, 2015

It can solve by using simple vector equation I.e ( resultant vector )

Manas Vongpivat
Dec 30, 2015

Pythagoras Theolem

Elbert Rasay
Oct 23, 2015

I'm just wondering if there's a specific name for this one. I remember calling the 3-4-5 right triangle combination an Egyptian triangle

Jonas Capili
Oct 10, 2015

Pythagorean theorem

Junaid Ghazali
Aug 12, 2015

it makes a shape of triangle. √12²+25²=13

Tushar Kaushik
Aug 10, 2015

Pythagoras theorm

Sreyash Roy
Aug 5, 2015

This problem is according to the Pythagoras theorem,

Kerry Grady
Jul 26, 2015

bad question. why assume park did not extend further south. distance could have been 12m assuming ll lines and park starting min of 5m south of walkers intersect.

Anurag Pandey
Apr 26, 2015

Simple use of Pythagoras's theorem .

Richard Pecson
Mar 1, 2015

a^2+b^2=c^2 5^2+12^2=c^2 25+144=c^2 169=c^2 13

Huy Nguyen
Feb 14, 2015

Just use Pythagorean Theorem. It's very easy!

Getachew Melese
Dec 31, 2014

Required distance is radical of 144+25 which is equal to 13 meter

Write a solution. 13

Jeremy Bansil
Aug 16, 2014

The Pythagorean theorem, which shows a 2 + b 2 = c 2 a^{2} + b^{2} = c^{2}

So 1 2 2 + 5 2 = 144 + 25 = 169 12^{2} + 5^{2} = 144 + 25 = 169 , then the square root of 169 169 is 13 \boxed{13}

Pythagoras theorem

hypotenuse

Jalees Mughal
Jul 23, 2014

Pythagoras theorem

suared? how is it? please answer my quistion cause icant sleep on it

Rj Gabini - 6 years, 10 months ago

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A turn represents, basically, a 90 degree angle.

a squared + b squared = c squared.

5 squared + 12 squared = c squared.

25 + 144 = c squared

169 = c squared

c = 13

Also, (5,12,13) is a Pythagorean Triple. It's easily identifiable. As such with (3,4,5), (8,15,17) and (7,24,25). Anyways. yeah.

Seany Mew - 6 years, 10 months ago
Anthony Teo
Jul 11, 2014

This is solved using the Pythagoras Theorem. So (5 squared) + (12 squared)= Distance from the park squared. 25+144=169. The square root of 169 is 13. So 13 is the answer.

Sorry Clavin, but strictly speaking, your answer is only approximate. In fact, we on the surface of the earth need to practice spherical trigonometry to solve problems like this "exactly". Sure, the error is small, but approximating a spherical triangle with a plane triangle is still an error... Remember that in a spherical surface geometry, there are no parallel lines (all lines meet eventually), straight lines are great circles, and angles of a triangle sum to more than 180 degrees.

Andrew Rakich - 6 years, 10 months ago

use phythagorean theorem, c2=a2+b2 , 0r c=square root of a2+b2

No one said that the left he took is perfectly normal (90 degrees)

Mina Fouad - 6 years, 11 months ago

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If the direction was other than perfect notmal, it would have been specified.

Chellappanpillai S. Radhakrishnan - 6 years, 11 months ago
Khen Camero
Jun 28, 2014

i try physics to solve this problems using the resultant vector .. and it's effective.

you are great bro!

Agustin Peñalosa Jr. - 6 years, 11 months ago
Iuki Nishikawa
Jun 24, 2014

Pythagorean Theorem. Formula: c^2 = b^2 + a^2 [where c is the hypotenuse, and b and a are the legs]

Solution:

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

/sqrt c^2 = /sqrt 169

c = 13

Krishna Garg
Jun 24, 2014

It is triangle with two sides of 5 and 12 meters and 90 degree angle.by pythogorous calculations,we get distance of park from his house 13 Meters ans.

K.K.GARG.India

pythagorean

Reshma Ramesh
Jun 23, 2014

simple pythagoras theorem.

5 ^2 + 12 ^2 = 169 ( 13 ^2). So the answer is 13

Jacob Samro - 6 years, 11 months ago
Kandarp Singh
Jun 23, 2014

/sqrt{25+144} = 13

\sqrt{25+144} = 13

Kandarp Singh - 6 years, 11 months ago

simple trignometry:.pythagoras theorem

Aditya Marisarla - 6 years, 11 months ago
Pablo Del Corral
Jun 23, 2014

It's just about using squares and roots

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