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vodomira [7]
2 years ago
14

Find the length of side x in simplest radical form with a rational denominator.

Mathematics
2 answers:
RideAnS [48]2 years ago
7 0

Answer:

Step-by-step explanation:

The tangent of a 60 degree angle = Sin(60) / Cos(60)

Sin(60) = Square root (3) / 2

Cos(60) = 1/2

Tan(60) = √3 / 2 // 1/2   Invert the denominator and multiply

Tan(60) = √3/2 * 2/1

Tan(60) = √3

Tan(theta) = opposite / adjacent

Tan(theta) = x/3 in this case

Tan(60) = √3 = x/3

x = 3*√3

pshichka [43]2 years ago
5 0

Answer:

3\sqrt{3}

Step-by-step explanation:

In all 30-60-90 triangles, the side lengths are in the ratio x:x\sqrt{3}:2x, where x is the side opposite to the 30 degree angle and 2x is the hypotenuse of the triangle. Since the side opposite to the 30 degree angle is marked as 3, the value of x must be \boxed{3\sqrt{3}}.

Alternatively, we can use basic trig. for a right triangle to solve. In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Thus, we have:

\tan 60^{\circ}=\frac{x}{3},\\x=3\tan 60^{\circ}=\boxed{3\sqrt{3}}

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