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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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The length of a rectangle is eight more than twice its width. The perimeter is 96 feet. Find the dimensions of the rectangle
Debora [2.8K]

Answer:

The width  of the rectangle is 14'8",  and the length is 33'4"

Step-by-step explanation:

We're given two pieces of information:

The length is eight more than twice the width:

l = 2w + 4

The perimeter is 96 feet:

p = 96

We also need to apply one more piece of information that is not provided here, and that is the relationship between the perimeter of a rectangle, and it's length and width:

p = 2l + 2w

We can solve for w by plugging the other two values into the last:

p = 2w + 2l\\96 = 2w + 2(2w + 4)\\96 = 2w + 4w + 8\\88 = 6w\\3w = 44\\w = \frac{44}{3}\\w = 14\frac{2}{3}

Now we can find the length by plugging w into the first equation:

l = 2w + 4\\l = 2(14\frac{2}{3}) + 4\\l = 29\frac{1}{3} + 4\\l = 33\frac{1}{3}

One third of  a foot is four inches, so the width is 14'8" and the length is 33'4"

To make sure our answer is correct, we should plug those numbers back into the area equation and see if we're right:

p = 2l + 2w\\p = 2(33\frac{1}{3}) + 2(14\frac{2}{3})\\p = 66\frac{2}{3} + 29\frac{1}{3}\\p = 96

So we know our answer's correct

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