Question

Из точки к плоскости проведены две наклонные АВ и АС найдите растояние от точки А до плоскости если АВ:АС=13:15 а длины проекций АВ и АС на плоскость равны 5см и 9см соответсвенно

Answer 1

Простите, но получилось как получилось.

Answer 2

Finding the Distance from Point A to the Plane

To find the distance from point A to the plane, we can use the formula:

Distance from point A to the plane = (|AB x AC|) / |AC|

where AB and AC are the vectors representing the two inclined lines, and |AB x AC| denotes the magnitude of the cross product of AB and AC.

Given that AB:AC = 13:15 and the lengths of the projections of AB and AC onto the plane are 5 cm and 9 cm respectively, we can determine the lengths of AB and AC.

Let's calculate the lengths of AB and AC:

AB = 13 * 5 cm = 65 cm AC = 15 * 9 cm = 135 cm

Now, we can calculate the distance from point A to the plane:

Distance from point A to the plane = (|AB x AC|) / |AC|

To find the cross product of AB and AC, we need to calculate the determinant of the matrix formed by the components of AB and AC:

AB = (65, 0, 0) AC = (0, 135, 0)

Calculating the determinant:

|AB x AC| = |(65, 0, 0) x (0, 135, 0)| = |(0, 0, 8775