A perpendicular AK to its plane is drawn through the vertex A of the right-angled triangle ABC
| April 15, 2021 | education
A perpendicular AK to its plane is drawn through the vertex A of the right-angled triangle ABC (angle C = 90 degrees). Find the distance from point K to straight line BC, if AK = 4, AB = 7, BC = root of 29.
AC ⊥ BC, AK ⊥ ABC => KC ⊥ BC as mutually perpendicular.
KC – the required distance from point K to line BC.
Received two right-angled triangles ABC (C = 90 °) and ACK (K = 90 °), with a common leg AC.
According to the Pythagorean theorem,
AC = √ (AB² – BC²) = √ (49 – 29) = √20.
KC = √ (AC² + AK²) = √ (20 + 16) = √36 = 6.
Answer: the distance from point K to line BC = 6.
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