Odpowiedź:
a = 16 b = 8 c > 0
α = 45°
więc
z tw. kosinusów
16² = 8² + c² -2*8*c*cos 45°
256 = 64 + c² - 16 c* 0,5 √2
256 = 64 + c² - 8√2 c
c² - 8√2 c - 192 = 0
Δ = 64*2 - 4*1*( - 192) = 128 + 768 = 896 = 64*14
√Δ = 8 [tex]\sqrt{14}[/tex]
c = [tex]\frac{8\sqrt{2} + 8\sqrt{14} }{2*1} = 4\sqrt{2} + 4\sqrt{14}[/tex]
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oraz z tw. sinusów
[tex]\frac{16}{sin 45^o} = \frac{8}{sin \beta }[/tex]
16 sin β = 8*sin 45° = 8*0,5√2 = 4√2 / : 16
sin β = [tex]\frac{\sqrt{2} }{4}[/tex] ≈ 0,3536
β ≈ 19,5°
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γ ≈ 180° - 45° - 19,5° = 115,5°
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Odpowiedź:
a = 16 b = 8 c > 0
α = 45°
więc
z tw. kosinusów
16² = 8² + c² -2*8*c*cos 45°
256 = 64 + c² - 16 c* 0,5 √2
256 = 64 + c² - 8√2 c
c² - 8√2 c - 192 = 0
Δ = 64*2 - 4*1*( - 192) = 128 + 768 = 896 = 64*14
√Δ = 8 [tex]\sqrt{14}[/tex]
c = [tex]\frac{8\sqrt{2} + 8\sqrt{14} }{2*1} = 4\sqrt{2} + 4\sqrt{14}[/tex]
----------------------------------------
oraz z tw. sinusów
[tex]\frac{16}{sin 45^o} = \frac{8}{sin \beta }[/tex]
16 sin β = 8*sin 45° = 8*0,5√2 = 4√2 / : 16
sin β = [tex]\frac{\sqrt{2} }{4}[/tex] ≈ 0,3536
β ≈ 19,5°
------------
γ ≈ 180° - 45° - 19,5° = 115,5°
------------------------------------------------
Szczegółowe wyjaśnienie: