In triangle ABC, angle A = α, angle C = β, BC = 7cm, HH-height. Find NA.

Since ВН is the height of triangle ABC, then triangles ABН and ВСН are rectangular.

In a right-angled triangle BCH, we determine the size of the ВН leg through the hypotenuse and the opposite VN angle.

Sinβ = HВ / HВ.

ВН = ВС * Sinβ = 7 * Sinβ see.

In a right-angled triangle ABН, we express the size of the leg AH through the leg BH and the angle ВAН.

tgα = BH / AH.

AH = BH / tgα = 7 * Sinβ / tgα see.

Answer: The length of the segment AH is equal to 7 * Sinβ / tgα cm.

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