In the triangle ABC, it is known that the angle C = 90 degrees, CD is perpendicular to AB
| April 2, 2021 | education
In the triangle ABC, it is known that the angle C = 90 degrees, CD is perpendicular to AB, BC = 3cm, CD = √8. Find the lengths of the sides AB, AC, DB.
From the right-angled triangle ВСD we determine the length of the VD leg using the Pythagorean theorem.
ВD ^ 2 = ВС ^ 2 – СD ^ 2 = 9 – 8 = 1.
ВD = 1 cm.
The height CD is drawn from the vertex of the right angle to the hypotenuse, then the square of its length is equal to the product of the segments into which it divides the hypotenuse.
CD ^ 2 = BD * AD.
AD = CD / BD = 8/1 = 8 cm.
Then AB = AD + BD = 8 + 1 = 9 cm.
From a right-angled triangle ABC, AC ^ 2 = AB ^ 2 – BC ^ 2 = 81 – 9 = 72.
AC = √72 = 6 * √2 cm.
Answer: The length of side AB is 9 cm, AC is 6 * √2 cm, DB is 1 cm.
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