In obtuse triangle ABC, AC = BC = 25, height AH is 20 Find cosACB.
| May 1, 2021 | education
By the Pythagorean theorem in a right-angled triangle ACH, we determine the length of the leg CH.
CH ^ 2 = AC ^ 2 – AH ^ 2 = 625 – 400 = 225.
CH = 15 cm.
Then BH = 25 + 15 = 40 cm.
In a right-angled triangle ABH, according to the Pythagorean theorem: AB ^ 2 = AH ^ 2 + BH ^ 2 = 400 + 1600 = 2000.
Then in the triangle ABC, by the cosine theorem:
AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AC * BC * CosACB.
2000 = 625 + 625 – 2 * 25 * 25 * CosABC.
1250 * CosABC = 1250 – 2000 = -750.
CosABC = -750 / 1250 = -0.6.
Answer: CosABC is – 0.6.
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