Question

usando as formulas seno, cosseno e tangente, determine o valor de x nas figuras abaixo? ​

Answer 1

Razões trigonométricas no triângulo retângulo

$\boxed{\boxed{\mathsf{seno=\dfrac{cateto~oposto}{hipotenusa}}}}\\\boxed{\boxed{\mathsf{cosseno=\dfrac{cateto~adjacente}{hipotenusa}}}}\\\boxed{\boxed{\mathsf{tangente=\dfrac{cateto~oposto}{cateto~adjacente}}}}$

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$\mathtt{a)}~\mathsf{sen(60^{\circ})=\dfrac{x}{50}}\\\mathsf{\dfrac{\sqrt{3}}{2}=\dfrac{x}{50}}\\\mathsf{2x=50\sqrt{3}}\\\mathsf{x=\dfrac{50\sqrt{3}}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=25\sqrt{3}}}}}}\\\mathtt{b)}~\mathsf{tg(60^{\circ})=\dfrac{12}{x}}\\\mathsf{\sqrt{3}=\dfrac{12}{x}}\\\mathsf{\sqrt{3}x=12}\\\mathsf{x=\dfrac{12}{\sqrt{3}}}\\\mathsf{x=\dfrac{12\sqrt{3}}{3}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=4\sqrt{3}}}}}}\\\mathtt{c)} ~\mathsf{cos(30^{\circ})=\dfrac{x}{50}}\\\mathsf{\dfrac{\sqrt{3}}{2}=\dfrac{x}{50}}\\\mathsf{2x=50\sqrt{3}}\\\mathsf{x=\dfrac{50\sqrt{3}}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=25\sqrt{3}}}}}}\\\mathtt{d)}~\mathsf{cos(20^{\circ})=\dfrac{15}{x}}\\\mathsf{0,93=\dfrac{15}{x}}\\\mathsf{x=\dfrac{15}{0,93}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{x=15,96}}}}}$

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