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Pechenushka12345
@Pechenushka12345
August 2022
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Найти тангенс угла AOB
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Kазак
По теореме Пифагора найдём длины всех трёх сторон
АО² = 8² + 6² = 64 + 36 = 100
ВО² = 7² + 1² = 50
АВ² = 7² + 1² = 50
По теореме косинусов
ВА² = ВО² + АВ² - 2*ВО*АВ*cos(∠ВОА)
50 = 50 + 100 -2√50*10*cos(∠ВОА)
100 =
2√50*10
*cos(∠ВОА)
10 =
2√50*cos(∠ВОА)
5 = 5
√2
*cos(∠ВОА)
cos(∠ВОА) = 1/√2
∠ВОА = arccos(1/√2) = 45°
tg(
∠ВОА) = 1
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Answers & Comments
АО² = 8² + 6² = 64 + 36 = 100
ВО² = 7² + 1² = 50
АВ² = 7² + 1² = 50
По теореме косинусов
ВА² = ВО² + АВ² - 2*ВО*АВ*cos(∠ВОА)
50 = 50 + 100 -2√50*10*cos(∠ВОА)
100 = 2√50*10*cos(∠ВОА)
10 = 2√50*cos(∠ВОА)
5 = 5√2*cos(∠ВОА)
cos(∠ВОА) = 1/√2
∠ВОА = arccos(1/√2) = 45°
tg(∠ВОА) = 1