Question

Dada a figura, calcule a medida do ângulo B.
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Answer 1

30º

Explicação passo-a-passo:

⇒ Lei dos senos

$\frac{AB}{sen45} = \frac{AC}{senB}$

OBS:

$sen45 = \frac{ \sqrt{2} }{2}$

Substituindo;

$\frac{20}{ \frac{ \</strong><strong>s</strong><strong>qrt{2} }{2} } = \frac{10 \sqrt{2} }{sen</strong><strong>B</strong><strong>}$

$20 \times sen</strong><strong>B</strong><strong> = 10 \sqrt{2} \times \frac{ \sqrt{2} }{2}$

$20 \times sen</strong><strong>B</strong><strong> = \frac{10 \sqrt{4} }{2}$

$20 \times sen</strong><strong>B</strong><strong> = \frac{10 \times 2}{2}$

$20 \times sen</strong><strong>B</strong><strong> = 10$

$sen</strong><strong>B</strong><strong> = \frac{10}{20}$

$sen</strong><strong>B</strong><strong> = \frac{1}{2}$

O seno do ângulo, cujo valor é 1/2 é o seno de 30º. Logo, o SenB = Sen30º.

Espero que eu tenha ajudado.

Bons estudos ! !