In a triangle ABC AB = 16 cm, angle A = 30, BK-perpendicular to the plane of the triangle.

In a triangle ABC AB = 16 cm, angle A = 30, BK-perpendicular to the plane of the triangle. Find BK if the distance from point K to AC is 17cm.

Let us draw the height BH from the vertex B of the triangle ABC. Then, in the formed right-angled triangle AH, the leg BH lies opposite the angle 30, and therefore is equal to half the length of the hypotenuse A.

BH = AB / 2 = 16/2 = 8 cm.

In a right-angled triangle KBH, the hypotenuse KH = 17 cm by condition, and the cathe BH = 8 cm by calculation, then, according to the Pythagorean theorem, the cathetus BK will be equal to:

BK ^ 2 = KH ^ 2 – BH ^ 2 = 17 ^ 2 – 8 ^ 2 = 289 – 64 = 225.

BK = √225 = 15 cm.

Answer: The length of the segment BK = 15 cm.