Odpowiedź:
zad.6
[tex]a = 8 \sqrt{2} \\ b = 17 \\ \\ h = \sqrt{ {b}^{2} - ( \frac{1}{2} d {)}^{2} } = \sqrt{ {17}^{2} - ( \frac{1}{2}a \sqrt{2} {)}^{2} } = \sqrt{289 - ( \frac{1}{2} \times 8 \sqrt{2} \times \sqrt{2} {)}^{2} } = \sqrt{289 - 64} = \sqrt{225} = 15 \\ \\ [/tex]
[tex] = \frac{1}{3} {a}^{2} \times h = \frac{1}{3} \times (8 \sqrt{2} {)}^{2} \times 15 = \frac{1}{3} \times 128 \times 15 = 640 {cm}^{3} [/tex]
zad.7
[tex]h = 5 \sqrt{3} \\ \\ tg3 {0}^{o} = \frac{ \frac{1}{2} d}{h} \\ \frac{ \sqrt{3} }{3} = \frac{ \frac{1}{2}d }{5 \sqrt{3} } \\ 15 = \frac{3}{2} d \\ d = 10[/tex]
[tex]d = a \sqrt{2} \\ 10 = a \sqrt{2} \\ a = \frac{10}{ \sqrt{2} } 5 \sqrt{2} [/tex]
[tex]v = \frac{1}{3} {a}^{2} \times h = \frac{1}{3} \times (5 \sqrt{2} {)}^{2} \times 5 \sqrt{3} = \frac{250 \sqrt{3} }{3} \: {cm}^{3} [/tex]
