5) Дано: \triangle DMP, \angle D=90 DM= 8 ; DP= 6,5 Найти: PM sin M, cos M, tg M ctg M

Ответ: PM = 10,3, sin M = 0,63, cos M = 0,77, tg M = 0,81, ctg M = 1,23

• Дано: \(\triangle DMP\), \(\angle D = 90°\), DM = 8, DP = 6,5
• Найти: PM, sin M, cos M, tg M, ctg M
• Решение:
  • По теореме Пифагора: PM = \(\sqrt{DM^2 + DP^2} = \sqrt{8^2 + 6.5^2} = \sqrt{64 + 42.25} = \sqrt{106.25} \approx 10.3\)
  • \(sin M = \frac{DP}{PM} = \frac{6.5}{10.3} \approx 0.63\)
  • \(cos M = \frac{DM}{PM} = \frac{8}{10.3} \approx 0.77\)
  • \(tg M = \frac{DP}{DM} = \frac{6.5}{8} \approx 0.81\)
  • \(ctg M = \frac{DM}{DP} = \frac{8}{6.5} \approx 1.23\)

Ответ: PM = 10,3, sin M = 0,63, cos M = 0,77, tg M = 0,81, ctg M = 1,23