From point A, inclined AB and AC equal to 12 cm and 18 cm are drawn to the plane. find the lengths of oblique projections

| February 7, 2021 | education

From point A, inclined AB and AC equal to 12 cm and 18 cm are drawn to the plane. find the lengths of oblique projections if one of the projections is 10 cm larger than the other.

Let the length of the projection of the inclined speaker onto the plane be equal to X cm, then, by condition, the length of the projection of the inclined AB onto the plane will be (X + 10) cm.

Let us drop the perpendicular AO from point A to the plane.

In the formed right-angled triangles AOB and AOS, the AO leg is common. Let us express this leg through the Pythagorean theorem for both triangles.

AO ^ 2 = AB ^ 2 – OB ^ 2 = 324 – (X + 10) ^ 2.

AO ^ 2 = AC ^ 2 – OC ^ 2 = 144 – X2.

Let’s equate the right-hand sides of both equations.

324 – X ^ 2 – 20 * X – 100 = 144 – X ^ 2.

20 * X = 324 – 244 = 80.

X = 80/20 = 4 cm.

OS = 4 cm.

ОВ = 4 + 10 = 14 cm.

Answer: OS = 4 cm, OB = 14 cm.



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