Ответ:
АВ=[tex]\sqrt{(4-3)^{2}+(6-5)^{2} } =\sqrt{1+1} =\sqrt{2}[/tex]
АС=[tex]\sqrt{(5-3)^{2}+(5-5)^{2} } =\sqrt{4} =2[/tex]
ВС=[tex]\sqrt{(5-4)^{2} +(5-6)^{2} } =\sqrt{1+1} =\sqrt{2}[/tex]
За теоремою косинусів:
ВС²=АВ²+АС²-2×АВ×AC×cosβ
(√2)²=(√2)²+2²-2×√2×2×cosβ
0=2²+4√2×cosβ
4√2×cosβ=4
cosβ=1/√2=√2/2
β=45°
∠A=45°
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Ответ:
АВ=[tex]\sqrt{(4-3)^{2}+(6-5)^{2} } =\sqrt{1+1} =\sqrt{2}[/tex]
АС=[tex]\sqrt{(5-3)^{2}+(5-5)^{2} } =\sqrt{4} =2[/tex]
ВС=[tex]\sqrt{(5-4)^{2} +(5-6)^{2} } =\sqrt{1+1} =\sqrt{2}[/tex]
За теоремою косинусів:
ВС²=АВ²+АС²-2×АВ×AC×cosβ
(√2)²=(√2)²+2²-2×√2×2×cosβ
0=2²+4√2×cosβ
4√2×cosβ=4
cosβ=1/√2=√2/2
β=45°
∠A=45°