Question

How do I solve this?

Answer 1

y = 8
`√(3)`

Explanation:

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

tan60° =
`√(3)`, hence

tan60° =
`(opposite)/(adjacent)` =
`(y)/(8)`

Multiply both sides by 8

8 × tan60° = y, so

y = 8
`√(3)` ← exact value

Answer 2

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