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What is the distance between the point P and the top of the pyramid?Consider a pyramid...

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nasirjam | Student, Grade 9 | (Level 2) Honors

Posted November 21, 2012 at 2:54 PM via web

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What is the distance between the point P and the top of the pyramid?

Consider a pyramid that has as its base an equilateral triangle with sides 100m each. Its three lateral faces are identical isosceles triangles with sides 500m each. From a point P on the ground (on the same plane as the base) the angle of elevation of the top of the pyramid is 30°. Find the distance of the point P from the top of the pyramid.

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mathsworkmusic | (Level 1) Educator

Posted November 22, 2012 at 6:53 PM (Answer #1)

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The distance from the centre of the pyramid to an apex (corner) of the base is given by

`d = 50/cos(30) = 57.7`

The height of the pyramid squared `h^2` is given by the length of one of the ridges squared minus `d_1^2`

ie, `h^2 = 500^2 - d_1^2`

`implies `  `h = sqrt(500^2 - d_1^2) = 497`

The distance of `P` from the top of the pyramid is then given by

` ``p = h/tan(30) = 860.233m`

The distance between P and the top of the pyramid is 860.233m

 

 

 

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