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Mika and Tyler are visiting the aquarium pyramid at Moody Gardens. From where Miko is standing , the angle of elevation to the top of the pyramid is 51.8 degrees. From Tyler's position the angle of elevation is 58 degrees. If they are standing 20 feet apart, and they are each 5feet 6inches tall, how tall is the pyramid?

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Nirina7
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scme1702
The closer we get to an object, the greater the angle of elevation becomes. Thus, Tyler is standing closer to the pyramid.
Let h be the height of the pyramid and x be Tyler's distance from the pyramid
Mika's distance = x + 20

We will now use:
tan(∅) = height / base

For Tyler:
tan(58) = h/x
x = h/1.6

For Mika:
tan(51.8) = h/(x + 20)
x + 20 = h / 1.27

Substituting x,
h/1.6 + 20 = h/1.27
1.27h + 40.64 = 1.6h
0.33h = 40.64
h = 123.2 feet
The height of the observers is 5.5 feet; thus the actual height of the pyramid is:
123.2 + 5.5
= 128.7 feet

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