From a point 8 cm away from the plane, an oblique and perpendicular are drawn

From a point 8 cm away from the plane, an oblique and perpendicular are drawn to the plane, the angle between which is 60 degrees. find the length of the slope.

According to the condition, point A is given 8 cm distant from the plane BC. From point A to the plane BC, an oblique AB and a perpendicular AC are drawn, the angle between which is 60 °.

Since the distance from a point to the plane is equal to the perpendicular dropped from this point to the plane, then AC = 8 cm.

Consider the resulting rectangular △ ABC: ∠C = 90 °, ∠A = 60 °, AC = 6 cm and BC – legs, AB – hypotenuse (since it lies opposite the right angle).

1. By the theorem on the sum of the angles of a triangle:

∠A + ∠B + ∠C = 180 °;

60 ° + ∠B + 90 ° = 180 °;

∠B = 180 ° – 60 ° – 90 °;

∠B = 30 °.

2. In a right-angled triangle, the leg opposite to an angle of 30 ° is equal to half the hypotenuse.

In this way:

AC = AB / 2;

AB / 2 = 8;

AB = 2 * 8;

AB = 16 cm.

Answer: AB = 16 cm.