In rectangular ΔABC Angle C = 90 degrees, CD – height, AC = 15 cm, AD = 9 cm.Find AB and sinA

univerkov | October 15, 2021 | education

By the Pythagorean theorem, we determine the length of the height СD.

CD ^ 2 = AC ^ 2 – AD ^ 2 = 225 – 81 = 144.

СD = 12 cm.

Right-angled triangles ACD and BCD are similar in acute angle, then AD / CD = BD / CD.

ВD = СD ^ 2 / АD = 144/9 = 16 cm.

Then AB = AD + BD = 9 + 16 = 25 cm.

Then CB ^ 2 = AB ^ 2 – AC ^ 2 = 625 – 225 = 400. CB = 20 cm.

SinBAC = CB / AB = 20/25 = 4/5

Answer: The length of side AB is 25 cm, SinA = 4/5.

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