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# Trigonometry

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the angle of elevation to the top of the Egyptian pyramid Cheops is 36.4°, measured from a point 350 feet from the base of the pyramid. The angle of elevation from the base of a face of the pyramid is 51.9°. Find the height of Cheops.

May 4, 2018

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Let the height of the pyramid  =  h

And let the distance from the face of the base to the point directly beneath the apex = x

So....we have two equations

tan(36.4)  =  h / (350 + x)       multiply both sides by (350 + x)

(350 + x) tan (36.4)  = h      (1)

And the second one is

tan (51.9)  = h / x

x* tan(51.9)  = h     (2)

Equating (1)  and (2), we have

(350 + x) * tan(36.4)   =  x * tan (51.9)     simplify

350*tan(36.4)  + x * tan (36.4)  = x * tan (51.9)

350* tan(36.4)  =    x* tan(51.9) - x * tan (36.4)

350*tan (36.4)  = x [ tan(51.9) - tan(36.4) ]

350 tan(36.4) / [ tan (51.9) - tan(36.4 ) ]   = x

x ≈ 479.558 ft

Using (2)  we can find the height as

479.558 * tan(51.9)  =  h ≈  611.6 ft

May 4, 2018