In a right-angled triangle ABC (angle C = 90 degrees) AB = 41 cm, AC = 9 cm.

In a right-angled triangle ABC (angle C = 90 degrees) AB = 41 cm, AC = 9 cm. Points M and K are the midpoints of sides AB and AC, respectively. Find: a) the length of the segment MK, b) tangents of acute angles.

By the Pythagorean theorem, we determine the length of the BC leg.

BC ^ 2 = AB ^ 2 – AC ^ 2 = 1681 – 81 = 1600.

BC = 40 cm.

Since the anguish of M and K are the middle of the sides AB and AC, then the segment MK is the middle line of the triangle ABC, then MK = BC / 2 = 40/2 = 20 cm.

Determine the tangent of the angle BAC.

tgBAC = BC / AC = 40/9 = 4 (4/9).

Then the tangent of the angle ABC = 1 / tgBAC = 9/40.

Answer: The length of the MK segment is 20 cm, the tangents of the acute angles are 4 (4/9) and 9/40.