On the HP side of the rectangle MHPK, in which MK = 41 and MH = 21, point A is marked
| February 11, 2021 | education
On the NP side of the rectangle MNPK, in which MK = 41 and MN = 21, point A is marked so that the angle MAN = 45 °. Find AK.
Since the MНРK is a rectangle, the MНA triangle is rectangular.
In a right-angled triangle IНA, one of the acute angles is 45, then the MНA triangle is isosceles, then HA = MH = 21 cm.
The length of the segment AР = HP – HA = 41 – 21 = 20 cm.
In a right-angled triangle AРC, according to the Pythagorean theorem, we determine the length of the leg AK.
AK ^ 2 = AP ^ 2 + PK ^ 2 = 400 + 441 = 841.
AK = 29 cm.
Answer: The length of the AK segment is 29 cm.
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