Geo5.4.4

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Find the distance between the points below

i). (-1,{\frac  {\pi }{8}}),({\sqrt  {2}},{\frac  {3\pi }{8}})\,

ii). (-3,45^{\circ }),(7,105^{\circ })\,

i). {\sqrt  {(-1)^{2}+({\sqrt  {2}})^{2}-2\cos {\frac  {3\pi }{8}}-{\frac  {\pi }{8}}}}\,

{\sqrt  {1+2+2{\sqrt  {2}}\cos {\frac  {\pi }{4}}}}={\sqrt  {3+2{\sqrt  {2}}({\frac  {1}{{\sqrt  {2}}}}}}\,

{\sqrt  {5}}\,

ii).{\sqrt  {9+49+42\cos 105-45}}={\sqrt  {58+42({\frac  {1}{2}})}}={\sqrt  {58+21}}={\sqrt  {80}}\,

4{\sqrt  {5}}\,


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