From points A and B, lying in 2 perpendicular planes, perpendiculars are omitted. AC and BD
| May 9, 2021 | education
From points A and B, lying in 2 perpendicular planes, perpendiculars are omitted. AC and BD are crossed by a plane on a straight line. Find the length of the segment AB, if AD = 5 cm, BC = 6 cm, CD = 4 cm
The ACD triangle is rectangular, since by condition, the AC line is perpendicular to the line of intersection of the planes.
By the Pythagorean theorem, we determine the length of the leg AC.
AC ^ 2 = AD ^ 2 – CD ^ 2 = 25 – 16 = 9.
AC = 3 cm.
AC is perpendicular to the plane BCD, then AC is perpendicular to BC, which means triangle ABC is rectangular.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 9 + 36 = 45.
AB = 3 * √5 cm.
Answer: The length of the segment AB is 3 * √5 cm.
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