Given an isosceles triangle ABC with leg equals 9 cm and base AC=12 cm. [br]The leg AB belongs to a plane [math]\alpha[/math] . [br]2 : 1 is the ratio of the orthogonal projections of the other sides  on [math]\text{$\alpha$ }[/math]. [br]Find the length of both projections and the angle between [math]\angle[/math]( [math]\alpha[/math]; (ABC))

Given a pyramid ABCDM with base ABCD - isosceles trapezoid. The perimeter of ABCD equals 32 cm and [math]\angle BAD=60^\circ[/math].[br]All lateral faces determine angles [math]75^\circ[/math] to the base.[br]Find the altitude of the pyramid

Given pyramid ABCDM with base ABCD - trapezoid. [br][math]\angle BAD=\angle ADC=90^\circ[/math], [math]\angle ABC=45^\circ[/math], [math]AB=a,[/math][br] [math]AM\bot\left(ABC\right)[/math] , [math]AM=2a[/math][br]Find [math]\angle\left(\left(ADM\right),\left(BMC\right)\right)[/math]=?

Given a regular quadrilateral pyramid ABCDE with base ABCD. If BD=[math]24\sqrt{2}[/math] and [math]\angle\left(\left(BCE\right),\left(DCE\right)\right)=120^\circ[/math], find the slant edge.

[math]ABCDA_1B_1C_1D_1[/math] - regular prism. If [math]AB=2[/math], [math]AA_1=\sqrt{6}[/math], find the distance from B[sub]1 [/sub]to (ACD[sub]1[/sub])