In a right-angled triangle ABC with a right angle C, the height CD is drawn, it is known that AD
| June 20, 2021 | education
In a right-angled triangle ABC with a right angle C, the height CD is drawn, it is known that AD = 3.2 cm, AC = 4 cm, find the non-marked sides of the triangle ABC.
Since CD is the height, the triangle ACD is rectangular in which, according to the Pythagorean theorem, we determine the length of the leg AD.
CD ^ 2 = AC ^ 2 – AD ^ 2 = 16 – 10.24 = 5.76.
CD = 2.4 cm.
CD is the height drawn from the top of the right angle to the hypotenuse, then CD ^ 2 = AD * BD.
BD = CD ^ 2 / AD = 5.76 / 3.2 = 1.8 cm.
AB = BD + AD = 1.8 + 3.2 = 5 cm.
By the Pythagorean theorem, BC ^ 2 = AB ^ 2 – AC ^ 2 = 25 – 16 = 9.
BC = 3 cm.
Answer: The length of the side AB is 5 cm, the length of the side AB is 5 cm, the height of CD is 2.4 cm.
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