To find the volume of a triangular pyramid with a side edge of 10 cm if the side edge makes with the basis plane a corner in 30 degrees.

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We find a projection of a side edge of AS to the basis. If the regular pyramid, then this projection of AO makes 2/3 heights of h of foundation of ABC. Then h = (3/2) *10*cos 30 ° = 15√3/2. The party and the bases is equal: and = h/cos 30 ° = (15√3/2)/(√3/2) = 15 cm. So Square of the basis is equal: So = a² √ 3/4 = 15² * √ 3/4 = 225√3/4 ≈ of 97.4279 cm ². Height of N of a pyramid is equal: N = 10*sin 30 ° = 10*(1/2) = 5 cm. The volume of the V pyramid is equal: V = (1/3) So*H = (1/3)*(225√3/4)*5 = 375√3/4 ≈ of 162.3798 cm ³.
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