Respuesta :

Danutz98

[tex]\text{The angle from the right is 30}^\circ \\ \\ \text{We use sinus theorem:}\\\\ \dfrac{y}{\sin(60)^{\circ}} = \dfrac{8}{\sin(30)^{\circ}} \Rightarrow \dfrac{y}{\dfrac{\sqrt{3}}{2}} = \dfrac{8}{\dfrac{1}{2}} \Rightarrow y = \dfrac{\sqrt 3}{2}\cdot 16\Rightarrow \boxed{y = 8\sqrt 3}[/tex]

Answer:

y = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex], hence

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{8}[/tex]

Multiply both sides by 8

8 × tan60° = y, so

y = 8[tex]\sqrt{3}[/tex] ← exact value