In a right-angled triangle ABC, the hypotenuse AB is 44cm. angle B is 30 ‘. CH is the height of the triangle.

In a right-angled triangle ABC, the hypotenuse AB is 44cm. angle B is 30 ‘. CH is the height of the triangle. Find the segments BH and AH.

Given:

right triangle ABC

angle C = 90 degrees

CH – height

AB = 4 cm

angle B = 30 degrees.

Find the lengths of the segments ВН, АН -?

Decision:

1. Consider a right-angled triangle ABC.

In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then BC = 1/2 * AB = 1/2 * 44 = 22 cm.

2. In a right-angled triangle, each leg is the average proportional between the hypotenuse and the projection of this leg onto the hypotenuse.

Then BC = √ (AB * HB);

22 = √ (44 * HB;

484 = 44 * HB;

HB = 484: 44;

HB = 11 cm.

3. So AH = AB – HB = 44 – 11 = 33 (cm).

Answer: 11 centimeters; 33 centimeters.