Point A is located on the face of the dihedral angle, the distance from it to the other face

| July 21, 2021 | education

Point A is located on the face of the dihedral angle, the distance from it to the other face is 1.94 dm, and to the edge is 3.26 dm. Find the angle

Let us denote the point of intersection of the perpendicular dropped from point A to another face by C, and the perpendicular to the edge of the dihedral angle by B.

The resulting triangle ABC will be right-angled with a right angle at the vertex C. Then, according to the condition, the side of the triangle is AC = 1.94, AB = 3.26.

By definition, in a right-angled triangle, the ratio of the length of the opposite leg to the length of the hypotenuse was called the sine of the angle.

Therefore: sin∠ABC = AC / AB = 1.94 / 3.26 ≈ 0.595.

∠ABC = arcsin0.595 ≈ 36.52 °.

Since ∠ABC is also the linear angle of the dihedral angle, it is equal to ≈ 36.52 °.



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