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Two bushwalkers are standing on different mountain sides. According to their maps, one of them is at a height of 2120m and the other is at a height of 1650m. If the horizontal between them is 950m, What is the direct distance between the two bushwalkers? 

 May 30, 2017
 #1
avatar+98197 
+1

 

We have a right triangle with the legs   =  (2120 - 1650)  = 470 m  and  950 m

 

And the direct distance between them  = the hypotenuse =   √ ( 470^2 + 950^2)  ≈  1059.9 m

 

 

 

cool cool cool

 May 30, 2017
 #2
avatar+132 
+7

The horizontal distance between the two points is 950m ( starting at 2120m). A vertical line can be drawn from the 1650m point joining it to the horizontal line.

The length of the vertical line will be:      2120 - 1650 = 470

Since we are looking for the direct distance, consider it to be a diagonal line. The horizontal line, the vertical line and the diagonal will make a triangle. The lengths of the first two are already given, therefore we are only required to find the diagonal ( which is also the direct distance). This can be done using the Pythagoras Theorum.

                                 a^2 + b^2 = c^2

                         950^2 + 470^2 = c^2

                                  1123400 = c^2

           square root of 1123400 = c

                                   1059.91 = c  (2 dp)

 May 30, 2017

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