In a right-angled triangle ABC, angle B is 90, AB = 4 cm, CB = 7 cm Find the distance: A) from point A to line BC

| April 2, 2021 | education

In a right-angled triangle ABC, angle B is 90, AB = 4 cm, CB = 7 cm Find the distance: A) from point A to line BC B) from point C to line AC Can the distance from point B to line AC be equal to 5 cm?

Since the triangle ABC is rectangular and the angle B = 900, the shortest distance from point A to straight line BC will be the segment AB = 4 cm.

Point C lies on line AC, then the distance from point C to line AC is zero.

By the Pythagorean theorem, we determine the length of the hypotenuse AC. AC ^ 2 = BC ^ 2 + AB ^ 2 = 47 + 16 = 65.

AC = √65 cm.

The area of the triangle ABC will be equal to: S = AB * BC / 2 = 7 * 4/2 = 14 cm.

The same mercy is equal to: S = AC * ВН / 2 = √65 * ВН / 2.

Then 14 = √65 * ВН / 2.

BH = 28 / √65 cm.

Answer: 4 cm, 0 cm, ВH cannot be 5 cm.



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