A plane is given. From point A, two inclined ones AB = 20 cm and AC = 15 cm are drawn to it.

| August 15, 2021 | education

A plane is given. From point A, two inclined ones AB = 20 cm and AC = 15 cm are drawn to it. The projection of the first inclined onto this plane is 16 cm. Find the projection of the second inclined.

The projection of point A onto the plane is the base of the perpendicular to this plane, dropped from point A. Then, since AO is perpendicular to the plane, and the projections of the inclined lie in this plane, then the segment OA is perpendicular to the projections OB and OC, and then the triangles AOB and AOC rectangular.

Determine the length of the leg AO from the right-angled triangle AOB.

AO ^ 2 = AB ^ 2 – BO ^ 2 = 400 – 256 = 144.

AO = 12 cm.

From the right-angled triangle AOC, we determine the length of the leg of the OC.

OC ^ 2 = AC ^ 2 – AO ^ 2 = 225 – 144 = 81.

OC = 9 cm.

Answer: The projection of the second oblique is 9 cm.



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