Răspunsuri

2014-04-04T12:51:24+03:00
In triunghiul CAD, D este de 90 grade. tgC = 3/4 => AD/CD = 3/4 dar CD=12 => AD/12=3/4 => AD=9. 
In triunghiul CAD, Pitagora > AC² = CD²+AD² => AC² = 12²+9² => AC²=144+81 => AC²=225 => AC=15

In triunghiul mare ABC , A este de 90 grade, tgC= 3/4 => AB/AC=3/4 => AB/15=3/4 => AB=45/4. 

In triunghiul ABD, D este de 90 grade, Pitagora > AB²=AD²+BD² => BD²=AB²-AD² => BD²=(45/4)²-9² => BD²= (45²-4²*9²)/16 => BD² = (2025 - 1296)/16 => BD² = 729/16 => BD²= (27/4)² => BD = 27/4. 
BC= BD+DC => BC=27/4+12=> BC=75/4

sinB=AC/BC iar cosB=AB/BC => sinB+cosB = (AC+AB)/ BC
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