Question

3) calcular os valores de a e b no triângulo abaixo:​

Answer 1

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$\sf tg(60^\circ)=\dfrac{b}{a}\\\sf \sqrt{3}=\dfrac{b}{a}\\\sf b=a\sqrt{3}\\\sf tg(30^\circ)=\dfrac{b}{a+12}\\\sf\dfrac{\diagup\!\!\!\!\!\sqrt{3}}{3}=\dfrac{a\diagup\!\!\!\!\!\sqrt{3}}{a+12}\\\sf 3a=a+12\\\sf 3a-a=12\\\sf 2a=12\\\sf a=\dfrac{12}{2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf a=6\checkmark}}}}\\\sf b=a\sqrt{3}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf b=6\sqrt{3}\checkmark}}}}}$