A. [tex]\sqrt{3}[/tex]
What is triangle and its properties?
In the Geometry, the triangle is a 3-sided polygon that consists of 3 edges and 3 vertices. The most important property of the triangle is that the sum of the internal angles of the triangle is = to 180 degrees. its property is known as angle sum property of triangle.
We have been given the image of the right triangle and we are asked to find the value of the tan(60) for our given triangle
from we know that tangent represents the relation between opposite or adjacent of the right triangle.
[tex]tan = \frac{opposite}{adjacent}[/tex]
We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we could conclude that our given triangle is 30-60-90 triangle.
from the sides corresponding to 30-60-90 triangle equals to[tex]x,x\sqrt{3}[/tex] and [tex]2x[/tex] , so the adjacent side for our given triangle will be,
[tex]x\sqrt{3} =8 \sqrt{3\\\\\\[/tex]
[tex]\frac{x \sqrt{3} }{\sqrt{3} } =\frac{8\sqrt{3} }{\sqrt{3} }[/tex]
[tex]x=8[/tex]
Upon substituting these values on above formula we will get,
[tex]tan( 60^{0} ) = \frac{8\sqrt{3} }{8} \\tan( 60^{0})=\sqrt{3}[/tex]
hence, the value of tan(60) is [tex]\sqrt{3}[/tex]and option B is the correct choice.
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