Given two perpendicular planes alpha and beta, point A is 8 cm away from alpha, and 17 cm

Given two perpendicular planes alpha and beta, point A is 8 cm away from alpha, and 17 cm from the line of intersection. Find: the distance from point a to Betta.

Consider the AH1O pattern.
Since АН1 is perpendicular to α, and AO is inclined to it, then Н1О is the projection of the inclined AO onto the α plane.
We get a right-angled triangle AH1O, where AO is the hypotenuse.
Hence OH1 = root of (17 ^ 2 – 8 ^ 2) = root (289 – 64) = 15.
Since α is perpendicular to β, OH1 is perpendicular to β.
By parallel transfer from ОН1, we obtain an equal segment coming out of A and perpendicular to β. This is the required distance from A to β.
Answer: 15