From point to plane, two inclined ones are drawn, the lengths of which are equal to 27cm and 29cm

From point to plane, two inclined ones are drawn, the lengths of which are equal to 27cm and 29cm, and their projections are related as 3: 4. Find oblique projections.

Two inclined ones drawn to one plane form a triangle, we represent it in the drawing as a triangle ABC.

From point A we draw a perpendicular to the plane, on the triangle it will fall to the base AB, we will designate it AK. He splits triangle ABC into 2 triangles – ABK and AKC.

These triangles are rectangular.

According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Let’s assume that 1 part – x cm

Considering that AK is a common side for right-angled triangles ABK and AKC, we will compose the equality:

Answer: inclined projections are 12 cm and 16 cm.