Question

Dado o triângulo ABC e o ângulo em C medindo 30°. A soma de x + y é igual a:

(A) 5 - 3^1/2
(B) 5 + 3^1/2
(C) 5 (1 - 3^1/2)
(D) 5 (1 + 3^1/2)
(E) 3 - 3^1/2

Answer 1

Resposta:

Item D

Explicação passo-a-passo:

$sen30=\dfrac{x}{10}\\\\\dfrac{1}{2}=\dfrac{x}{10}\\\\\\x=\dfrac{10}{2}\\\\x=5$

$cos30=\dfrac{y}{10}\\\\\dfrac{\sqrt{3}}{2}=\dfrac{y}{10}\\\\y=\dfrac{10\sqrt{3}}{2}\\\\y=5\sqrt{3}\\ \\\\\\logo\\\\x+y=5+5\sqrt{3}=5(1+\sqrt{3})$

Item D