Question

08- Considerando o triângulo retângulo ABC da figura, determine a medida de a + b

A) 36 m B) 39 m C ) 36 m D) 35 m


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Answer 1

Explicação passo-a-passo:

• $\sf sen~60^{\circ}=\dfrac{cateto~oposto}{hipotenusa}$

$\sf \dfrac{\sqrt{3}}{2}=\dfrac{12\sqrt{3}}{a}$

$\sf a\sqrt{3}=12\sqrt{3}\cdot2$

$\sf a\sqrt{3}=24\sqrt{3}$

$\sf a=\dfrac{24\sqrt{3}}{\sqrt{3}}$

$\sf a=24~m$

• $\sf tg~60^{\circ}=\dfrac{cateto~oposto}{cateto~adjacente}$

$\sf \sqrt{3}=\dfrac{12\sqrt{3}}{b}$

$\sf b\sqrt{3}=12\sqrt{3}$

$\sf b=\dfrac{12\sqrt{3}}{\sqrt{3}}$

$\sf b=12~m$

Logo:

$\sf a+b=24+12$

$\sf \red{a+b=36~m}$

Letra C