In a right-angled triangle, the hypotenuse is 4 cm, and the acute angle is 30 °.

In a right-angled triangle, the hypotenuse is 4 cm, and the acute angle is 30 °. The height drawn from the vertex of the right angle divides the hypotenuse into 2 segments. Find the lengths of these lines.

In a triangle ABC <B = 30, <C = 90. In a right-angled triangle opposite an angle of 30 degrees lies a leg equal to half of the hypotenuse. So AC = AB / 2.

AC = 4/2 = 2 (cm)

In triangle ABC we will draw the height of CO. Point O divides the segment AB into two parts AO and BO, which we need to find.

In a triangle ABC <A = 60 (<A + <B + <C = 180, the sum of the angles of the triangle is 180 degrees).

Angle A in triangle AOC is also 60 degrees, which means <ACO = 30. Opposite this angle lies the leg AO. AO = AC / 2.

AO = 2/2 = 1 (cm) s

BO = AB – AO; BО = 4 – 1 = 3 (cm).

Answer. 1 cm, 3 cm.