In an obtuse triangle ABC AB = BC = 9 roots of 5, the height AH is 18. Find tgACB.
| September 19, 2021 | education
In a right-angled triangle BCH, according to the Pythagorean theorem, we determine the length of the leg CH.
CH ^ 2 = BC ^ 2 – BH ^ 2 = (9 * √5) ^ 2 – 18 ^ 2 = 405 – 324 = 81.
CH = 9 cm.
Determine the tangent of the BCH angle.
tgBCH = BH / CH = 18/9 = 2.
Angles АСВ and ВСH are adjacent angles, then angle АСВ = (180 – ВСН).
Then tgACB = tg (180 – BCH) = -tgBCH = – 2.
Answer: The tangent of the ACB angle is -2.
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