<prompt> Katika mchoro ulio hapa chini, overrightarrowOA 1, arrowoverrightOB 1, na arrowoverrightOC sqrt2. Pia, tan angle AOC 7 na angle BOC 45circ.asyukubwa wa kitengo 2 cm;jozi A, B, C, O;A 1,0;B -0.6,0.8;C 0.2,1.4;O 0,0;choraO--A,Arrow6;choraO--B,Arrow6;choraO--C,Arrow6;leboA, A, E;leboB, B, NW;leboC, C, N;leboO, O, S;asyKuna viwango vya kudumu m na n ili hivyooverrightarrowOC m overrightarrowOA n overrightarrowOB.Ingiza jozi iliyoagizwa m,n.  <response>: Kwa kuunda pembetatu ya kulia na upande wa 1 unaopakana, upande wa 7, na hypotenuse sqrt12 72 5 sqrt2, tunaona hivyo.cos angle AOC frac15 sqrt2 quad textna quad sin angle AOC frac75 sqrt2. Kishaanzaaligncos pembe AOB cos pembe AOC pembe BOC cos pembe AOC cos pembe BOC - dhambi pembe AOC dhambi pembe BOC frac15 sqrt2 cdot frac1sqrt2 - frac75 sqrt2 cdot frac1 sqrt2 -frac35.endalignKuchukua bidhaa ya nukta ya equation overrightarrowOC m overrightarrowOA n overrightarrowOB with overrightarrowOA, tunapataarrow overrightarrowOA cdot overrightarrowOC m overrightarrowOA cdot overrightarrowOA n overrightarrowOA cdot overrightarrowOB.Kisha mshale wa kulia juuOA arrowoverrightOC cos angle AOC m arrow overrightarrowOA2 n overrightarrowOA arrowoverrightOB cos pembe AOB, aufrac15 m - frac35 n.Kuchukua bidhaa ya nukta ya mlinganyo overrightarrowOC m overrightarrowOA n overrightarrow OB pamoja na overrightarrowOB, tunapataarrow overrightarrowOB cdot overrightarrowOC m overrightarrowOA cdot overrightarrowOB n overrightarrowOB cdot overrightarrowOB.Kisha mshale wa kuliaOB arrowoverrightOC cos pembe BOC m mshale wa kulia kupita kiasiOA arrowoverrightOB cos pembe AOB n mshale wa kulia juuOB2, au1 -frac35 m n.Kutatua mfumo frac15 m - frac35 n na 1 -frac 35 m n, tunapata m,n left frac54, frac74 kulia. 