In ∆АВС ∠С = 30 °, АС = 82 cm, ВС = 18 cm. A straight line a is drawn through the vertex А

| January 2, 2021 | education

In ∆АВС ∠С = 30 °, АС = 82 cm, ВС = 18 cm. A straight line a is drawn through the vertex А, parallel to ВС. Find the distance between straight lines a and BC.

1. To find the distance from straight line a to straight line ВС, it is necessary to lower the height АН from the top А ∆АВС to the side ВС. (because to find the distance between || straight lines, you need to select a point on one of them and drop the perpendicular to the other)
2. Next, consider the resulting triangle ANS – rectangular (angle H = 90, since ASh is the height by construction).
1) AC – hypotenuse and AC = 82 cm. Angle C = 30. AH – leg, which lies opposite the angle of 30 degrees. This means that AH is equal to half of the hypotenuse AC, that is, AH = 82: 2 = 41 cm, and this is the required distance between straight lines a and BC.
Answer: the distance between straight lines a and BC = 41 cm.



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