The base of the AC of an isosceles triangle lies in the alpha plane. Find the distance from point B to the alpha plane if AB = 20 cm, AC = 24 cm, and the dihedral angle between the ABC and alpha planes is 30 degrees.
Since triangle ABC is isosceles and its sides are equal to AB = 20 cm and AC = 24 cm, we will find the height of this triangle by the Pythagorean theorem:
BK ^ 2 = AB ^ 2 – AK ^ 2.
BK = √ (20 ^ 2 – 12 ^ 2) = √ (400 – 144) = √256 = 16 cm.
The length of АK is equal to half of the side of АС, since triangle ABC is isosceles and then the height ВК = 16 cm.
Based on the condition, we are given a dihedral angle, this is the angle between the straight line BK and the plane alpha, the angle BKO.
We need to find BО since the angle BKO = 30 ° and BK = 16 cm, then the leg lying opposite 30 ° is equal to half of the hypotenuse, that is, BО = 16/2 = 8 cm.
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