The height CH of a right-angled triangle ABC halves the right angle C. Find the distance from

| June 19, 2021 | education

The height CH of a right-angled triangle ABC halves the right angle C. Find the distance from point C to line AB if the larger leg is 10 cm.

If the height of a right-angled triangle divides the right angle in the ratio of 2/1, then let the value of the angle ВСН = X0, then the value of the angle АСН = 2 * X0.

Then the angle (ВСН + АСН) = 90.

(X + 2 * X) = 90.

3 * X = 90.

X = BCH = 30.

Angle ACH = 90 – 30 = 60.

In a right-angled triangle ACН, the angle СAН = (90 – 60) = 30, and then the leg CH, pressing against this angle is equal to half the length of the AC.

CH = AC / 2 = 10/2 = see.

If the height of a right-angled triangle divides the right angle in half, then triangle ABC is right-angled and isosceles, then the angle BCН = ACН = 45, and triangle ACН is also right-angled and isosceles.

Then 2 * CH ^ 2 = AC ^ 2.

CH ^ 2 = 100/2 = 50.

CH = 5 * √2 cm.

Answer: The height of the triangle is 5 cm or 5 * √2 cm.



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