In the triangle MNK, it is known that MN = NK MK = 10, tgK = 0.8. Find the height NP of the given triangle.

Triangle MNK – isosceles (MN = NK).
The height NP of an isosceles triangle bisects the base:
PK = MK / 2.
In a right-angled triangle NPK, the ratio of legs NP and PK is tgK:
NP / PK = tgK;
NP = PK * tgK;
NP = (MK / 2) * tgK;
Substitute the values:
NO = (10/2) * 0.8 = 4 cm.
Answer: The height of the triangle is 4 cm.