# In a right-angled triangle ABC with a right angle C, the height CD is drawn.

In a right-angled triangle ABC with a right angle C, the height CD is drawn. It is known that BD = 25/13 dm, BC = 5 dm. Find the unknown sides of triangle ABC.

Since CD is the height of triangle ABC, triangles BCD and ACD are rectangular.

In the triangle ВСD, then by the Pythagorean theorem we define the length of the side СD.

CD ^ 2 = BC ^ 2 – BD ^ 2 = 25 – 625/169 = 3600/169.

CD = 60/13 dm.

Since the height CD is drawn from the top of the right angle, then CD ^ 2 = BD * AD.

AD = CD ^ 2 / BD = (3600/169) / (25/13) = 144/13.

Then AB = BD + AD = 25/13 + 144/13 = 169/13 dm.

In a right-angled triangle ACD, we determine the length of the hypotenuse AC.

AC ^ 2 = CD ^ 2 + AD ^ 2 = 3600/169 + 20736/169 = 24336/169.

AC = 156/13 dm.

Answer: The AB side is 169/13 dm, the AC side is 156/13 dm, the CD height is 60/13 dm.

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