In triangle ABC, angle A = angle B = 45 ° and AB = 19cm. find: 1) the distance from point C to line AB;

| July 19, 2021 | education

In triangle ABC, angle A = angle B = 45 ° and AB = 19cm. find: 1) the distance from point C to line AB; 2) the length of the projection of the segment AC on the straight line AB.

Since a triangle has two angles of 45 °, it means that the triangle is right-angled. Angle C = 90 °.

The distance from C to straight line AB will be designated by CD, for a triangle this distance will be the height. And in an isosceles triangle, the height drawn to the base is also the median. So AD = 19: 2 = 9.5 cm. Consider a triangle ACD, in it the angle is A = 45 °, the angle is D = 90 °, so the angle is C = 45 °. We get that the triangle ACD is isosceles, which means AD = CD = 9.5 cm.

Answer: the distance from straight line AB to point C = 9.5 cm; the length of the projection of the segment AC on the straight line AB = 9.5 cm.



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