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## Triangle problem – finding height with given area and angles.

If the area of triangle ABC is ${\cal S}$ and angles $\angle A= \alpha$ and $\angle B= \beta$ then find a altitude of triangle which drawn from C to AB.

HINT: Let altitude be h. $AC = \frac{h}{ \sin \beta } \; and \; BC = \frac{h}{ \sin \alpha } \; \angle ACB = \pi - \alpha - \beta$