Question

ABCDE is a square-based pyramid with vertex E directly above the center of the face ABCD. AB = 5 cm; AE = 7 cm.
a. Determine the angle a between the segment AE and the plane face ABCD. Sketch a diagram.
b. Determine the angle b between the plane face BCE and the plane face ABCD. Sketch a diagram.

Answer 1

Step-by-step explanation:

Let the midpoint of AC be M and the midpoint of AD be N. Then AC is perpendicular to EM. We can find the length of NE using Pythagoras:

NE=

√

82−1.52

=

√

247

2

Now we need to find ∠ENM

Again, since ENM forms a right angled triangle, ∠ENM=arccos(

1.5

√

247

2

)=78.9955...≈79degrees

I can include a diagram if this is hard to follow.

Edit: diagram included: