In a right-angled triangle ABC: angle A = 90, AB = 20, height AH = 12. find AC and cos of angle C.

univerkov | August 15, 2021 | education

Consider a right-angled triangle ADB, whose angle D is straight, hypotenuse AB = 20 cm, leg AD = 12 cm. Determine leg BD according to the Pythagorean theorem. BD ^ 2 = AB ^ 2 – AD ^ 2 = 20 ^ 2 – 12 ^ 2 = 400 – 144 = 256.BD = 16 cm.

Consider a right-angled triangle ABC and, using the formula for the proportionality of segments in a right-angled triangle, determine the segment CD.

AD ^ 2 = BD * CD.

СD = АD ^ 2 / ВD = 12 ^ 2/16 = 9 cm.

Consider a right-angled triangle ADC and find the hypotenuse AC.

AC ^ 2 = AD ^ 2 + DC ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225.

AC = 15 cm.

Let’s define Cos C.

Cos C = AC / BC = 15/25 = 3/5.

Answer: AC = 15 cm. Cos C = 3/5.

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