Answer:
103√3 units
Explanation:
To find the value of the missing side X, we can use the definition of a trigonometric ratio. In this case, since we are given the angle and the length of the side opposite to that angle, we can use the tangent ratio.
The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this triangle, the tangent of angle Y is:
tan(Y) = opposite side / adjacent side
Substituting the given values, we get:
tan(60°) = Y / X
We are given that Y = 309, so we can substitute that value in:
tan(60°) = 309 / X
To find the value of X, we can solve for X by dividing both sides of the equation by the tangent of 60°:
X = 309 / tan(60°)
The exact value of the tangent of 60° is √3, so we can substitute that in:
X = 309 / √3
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and the denominator by √3:
X = (309 * √3) / (√3 * √3)
X = 309√3 / 3
X = 103√3
Therefore, the length of the missing side X is 103√3 units.
