In an acute-angled triangle ABC, the heights AK and CE are drawn, CE = 12 cm, BE = 9cm, AK = 10cm. Find the AC.
| September 14, 2021 | education
In a right-angled triangle BCE, according to the Pythagorean theorem, we determine the length of the hypotenuse BC.
BC ^ 2 = CE ^ 2 + BE ^ 2 = 144 + 81 = 225.
BC = 15 cm.
Determine the area of the triangle ABC.
Savs = BC * AK / 2 = 15 * 10/2 = 75 cm2.
Through the area of the triangle ABC and the height CE, we determine the length of the side AB
Savs = AB * CE / 2.
AB = 2 * Savs / CE = 2 * 75/12 = 12.5 cm.
Then the segment AE = AB – BE = 12.5 – 9 = 3.5 cm.
In a right-angled triangle ACE, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.
AC ^ 2 = CE ^ 2 + AE ^ 2 = 144 + 12.25 = 156.25.
AC = 12.5 cm.
Answer: The length of the speaker side is 12.5 cm.
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