A plane intersects this rectangular pyramid perpendicular to the pyramid’s base and through its vertex. Which two-dimensional fi
gure is the cross section that results?
A. rectangle
B. hexagon
C. triangle
D. trapizoid
A. rectangle
B. hexagon
C. triangle
D. trapizoid
1 answer:
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We will use trigonometric identities to solve this. I will use θ (theta) for the angle.
First of all, we know that cotθ = 1/tanθ. This is a trigonometric identity.
We can replace cotθ in the expression with 1/tanθ.
Simplify: 1/tanθ * tanθ = tanθ/tanθ = 1
So now, we have:
Next, we also know that secθ = 1/cosθ. This is another trigonometric identity.
We can replace secθ with 1/cosθ in our expression.
Simplify:
Our third trigonometric identity that we will use is tanθ = sinθ/cosθ.
We can replace sinθ/cosθ with tanθ.
Now we have as our final answer:
Hope this helps!