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# Help Explain how to set up the equation that solves it PLEASE!

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1.  The solid in the diagram was formed by removing a corner from a cube with side lengths of 24cm. The length of EB of 6cm. Calculate the measure of angle PER Dont know how to set up the Cosine Equation to solve this...

Feb 14, 2019

#1
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Check page 7 of this. If it is confusing, I will try to work you through the process.

Feb 14, 2019
#2
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This is still confusing

Feb 14, 2019
#3
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After 2 hours:

RE^2 =18^2+24^2     (24 side length- 6 BE= 18)

RE=30 PR^2=24^2+24^2

PR=33.94112.....

Cos(PER)=30^2+30^2-33.9411...^2 / 2 (30) (30)

cos(PER) = 0.36

acos (0.36) = Angle PER

PER = 68.899803975907 degrees

HOPE THIS IS IT....... Please confirm

Feb 14, 2019
edited by StarStrike  Feb 14, 2019
#4
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Conside the line from E to RC that is parallel to BC.     Let the point of intersection be X

EX=24

XR=24-6=18

find ER

$$ER=\sqrt{24^2+18^2}\\ ER=\sqrt{900}\\ ER=30$$

Now PR is just the diagonal of one side of the square

$$PR=\sqrt{24^2+24^2}\\ PR=\sqrt{1152}\\$$

Now I have all 3 sides of the triangle so I can use cosine rule to find the angle between them

the sides are      $$30, \quad30, \quad \sqrt{1152}$$

$$1152=900+900-2*900*Cos(PER)\\ 1152=1800-1800*Cos(PER)\\ -648=-1800*Cos(PER)\\ 0.36=Cos(PER)\\ \angle{PER}=cos^{-1}0.36=68.8998^\circ=68^\circ54'$$

That is assuming I've not made any stupid mistakes.

Feb 14, 2019
#5
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You beat me to it StarStrike!

Good Work!

Feb 14, 2019
#6
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Thanks Melody!

StarStrike  Feb 14, 2019