Pyramid SABC has right triangular base ABC, with ∠ A B C = 90 ∘...

Paxton Hoffman

Paxton Hoffman

Answered

2022-07-23

Pyramid SABC has right triangular base ABC, with A B C = 90 . Sides A B = 3 , B C = 3. Lateral lengths are equal and are equal to 2. Find the angle created by lateral length and the base.

Answer & Explanation

dtal50

dtal50

Expert

2022-07-24Added 10 answers

Step 1
Let K be a middle point of AC.
Just S B K = S A K = arccos 3 2 = 30 ..
BK is a median of Δ A B C and is not perpendicular to AC, otherwise A B = B C, which is a contradiction.
By the way, B K S K, but we said about it in the first line.
Step 2
Let SK′ be an altitude of the pyramid.
Thus, since S A = S B = S C, we obtain: ΔSAK′≅ΔSBK′ and Δ S A K Δ S C K , which gives A K = B K = C K ,, which says K′ is a center of the circumcircle for Δ A B C.
Thus, K K.

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