Section 1.21  Interactive checkpoint: trigonometry  
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The great pyramid of Cheops has a square base with edges that are almost exactly 230 m long. The side faces of the pyramid make an angle of 51.8° with the ground.
The apex of the pyramid is directly above the center of the base. Find its height.
 
 

Answer:

h = m

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Diagram  [Hide]

Variables  [Hide]

Fill in the known values.

Variable

Value
length of edges of base

b = m

angle between pyramid faces and ground

θ = °

length of leg adjacent to angle

l

height of pyramid

h

I think I'm done. I need help. Show the correct values.
 
Strategy  [Hide]
  1. Find a suitable right triangle.
  2. Use a trigonometric function to relate the sides of the triangle and the given angle.
Physics principles and equations  [Hide]

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

c2 = a2 + b2

Step-by-step solution   [Hide]

Find the triangle

See the diagram if you are having trouble visualizing the triangle.

Calculate the leg length

Compute the length of the leg adjacent to the given angle, which is one-half the length of an edge of the base.

l = b / 2

l = ( m) / 2

l = m
3

Select an equation relating the legs of the triangle with the given angle.

Substitute variables

For this problem,

tan θ = h / l

Find h

h = l tan θ

h = (115 m)(tan °)

h = m

 

  
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