1)PR = ✓(QP²+QR²) = ✓4+16 = ✓20 = 2✓5
2) PO=OR = ✓5
3)cos QRP = QR/RP = 4/2✓5 = 2/✓5
4)Теорема косинусов для треугольника QOR:
QO² = QR²+OR² - 2QR•OR•cosQRP = 16+5 - 2•4•✓5•2/✓5 = 21-16 = 5
QO = ✓5
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Answers & Comments
1)PR = ✓(QP²+QR²) = ✓4+16 = ✓20 = 2✓5
2) PO=OR = ✓5
3)cos QRP = QR/RP = 4/2✓5 = 2/✓5
4)Теорема косинусов для треугольника QOR:
QO² = QR²+OR² - 2QR•OR•cosQRP = 16+5 - 2•4•✓5•2/✓5 = 21-16 = 5
QO = ✓5