Sierra walks 26 cubits due south, then 70 cubits due east and finally 50 cubits due north. How far is Sierra from her starting point?

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Answer 1 · 2018-01-24T21:42:04

$70$ $70$ Cubits.

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From the diagram:

$A B = 26$ $AB=26$ cubits due south.

$B C = 70$ $BC=70$ cubits due east.

$C E = 50$ $CE=50$ cubits due north

$A D$ $AD$ is parallel to $B C$ $BC$ and of equal length.

$D E = C E - C D = 24$ $DE=CE-CD=24$

We need to find $A E$ $AE$

By Pythagoras' theorem:

${(A D)}^{2} + {(D E)}^{2} = {(A E)}^{2}$ $(AD)^2+(DE)^2=(AE)^2$

${(70)}^{2} + {(24)}^{2} = {(A E)}^{2}$ $(70)^2+(24)^2=(AE)^2$

$5476 = {(A E)}^{2}$ $5476=(AE)^2$

$A E = \sqrt{5476} = 74$ $AE=sqrt(5476)=74$

Sierra is $70$ $70$ cubits from her starting position.