In a right-angled triangle ABC, Angle C is 90 ° CD-height, AC = 3 cm CD = 2.4 cm. Find AD.

univerkov | June 16, 2021 | education

Since the segment CD is the height of the ABC triangle, it divides it into two right-angled triangles ACD and BCD.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the leg AD.

AD ^ 2 = AC ^ 2 – CD ^ 2 = 9 – 5.76 = 3.24.

AD = 1.8 cm.

CD – the height of a right-angled triangle, drawn from the top of the right angle, then CD ^ 2 = AD * BD.

ВD = СD ^ 2 / АD = 5.76 / 1.8 = 3.2 cm.

Then AB = BD + AD = 3.2 + 1.8 = 5 cm.

Answer: AB = 5 cm, AD = 1.8 cm.

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