Option B: 13.9 is the value of y
Explanation:
Given triangle is a right angled triangle.
The legs of the triangle are 8 and y.
The hypotenuse of the triangle is x.
And the angle opposite to y is 60°
We need to determine the value of y.
Let us find the value of y using the tangent formula.
The formula for tan is given by
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Since, we know that [tex]\theta = 60^{\circ[/tex] , [tex]opp=y[/tex] and [tex]adj=8[/tex]
Substituting these values in the formula, we get,
[tex]tan \ 60^{\circ}=\frac{y}{8}[/tex]
Multiplying both sides by 8, we have,
[tex]8\times tan \ 60^{\circ}=y[/tex]
Substituting the value of [tex]\tan 60^{\circ}[/tex] , we get,
[tex]8\times 1.732=y[/tex]
Simplifying, we have,
[tex]13.856=y[/tex]
Rounding off, we get,
[tex]13.9=y[/tex]
Thus, the value of y is 13.9
Hence, Option B is the correct answer.
