# In a rectangular triangle ABC, the height CH is drawn, the angle C = 90 °.

August 24, 2021 | education

| **In a rectangular triangle ABC, the height CH is drawn, the angle C = 90 °. Find the lengths of the legs, the triangle if CH = 2.4 AH = 1.8, a BH = 3.2**

Since CH is the height of the triangle ABC, the triangles ACN and BCH are rectangular.

In a right-angled triangle ACН, according to the Pythagorean theorem, we determine the length of the hypotenuse AC. AC ^ 2 = AH ^ 2 + CH ^ 2 = 3.24 + 5.76 = 9.

AC = 3 cm.

In a right-angled triangle ВСН, according to the Pythagorean theorem, we determine the length of the hypotenuse BC. BC ^ 2 = BH ^ 2 + CH ^ 2 = 10.24 + 5.76 = 16.

BC = 4 cm.

Answer: The lengths of the legs of the triangle are 3 cm and 4 cm.

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