Question

Calcule o seno, o cosseno e a tangente de B.​

Answer 1

$(6 \sqrt{5} )^{2} = {6}^{2} + {x}^{2} \\ {x}^{2} = 36 \times 5 - 36 \times 1 \\ {x}^{2} = 36 \times 4 \\ {x}^{2} = {6}^{2} \times {2}^{2} \\ x = 12$

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$\cos( \beta ) = \frac{8}{12} \\ \cos( \beta ) = \frac{2}{3}$

$\sin^{2} ( \beta ) + \cos^{2} ( \beta ) = 1 \\ \sin^{2}( \beta ) = 1 - \frac{4}{9} = \frac{9 - 4}{9} = \frac{5}{9} \\ \sin( \beta ) = \frac{ \sqrt{5} }{3}$

$\tan( \beta ) = \frac{ \sqrt{5} }{2}$