In a right-angled triangle ABC, the angle is B = 90 degrees, AB = 8cm, AC = 16cm.

| June 20, 2021 | education

In a right-angled triangle ABC, the angle is B = 90 degrees, AB = 8cm, AC = 16cm. Find the angles that the height BH makes with the legs of the triangle.

1. In accordance with the properties of a right-angled triangle, the length of the leg, located opposite an angle of 30 °, is equal to half the length of the hypotenuse. The length of the leg AB is equal to half the length of the hypotenuse AC: AC / AB = 8: 16 = 1/2. Therefore, the angle C is 30 °.

2. We calculate the value of the angle СBН, taking into account that the sum of the angles of the triangle is 180 °:

Angle СBН = 180 ° – 30 ° – 90 ° = 60 °.

3. Angle ABH = 90 ° – 60 ° = 30 °.

Answer: The angle ABH between the height BH and leg AB is 30 °, the angle CBH between the height BH and leg BC is 60 °.



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