The height CH of a right-angled triangle ABC divides the right angle C in a ratio of 2: 1.

| June 3, 2021 | education

The height CH of a right-angled triangle ABC divides the right angle C in a ratio of 2: 1. Find the distance from point C to line AB if the larger leg of the triangle ABC is 10 cm.

Let’s use the picture to solve the problem.

According to the condition, the height of the CH divides the right angle ACB into two angles in a ratio of 2: 1, then the angle ACH will be equal to (90/3) * 2 = 60, and the angle HCB = (90/3) * 1 = 30.

Consider a triangle ACH, in which the angle CHA = 90, ACH = 60, then the angle CAH = 180 – 90 – 60 = 30. Since the leg CH of a right-angled triangle ACH is located opposite an angle of 30, its value is equal to half the length of the hypotenuse AC. CH = AC / 2 = 10/2 = 5 cm.

The distance from point C to line AB is 5 cm.

Answer: 5 cm.



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