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sasho [114]
3 years ago
5

Find the value of the variables. If your answer is not an integer, leave it in simplest radical form.

Mathematics
1 answer:
stepladder [879]3 years ago
4 0

We know that we can use trigonometry to solve for x here.

If we use tangent, we can solve for x directly:

tan(theta)=\frac{opposite}{adjacent}

tan(60)=\frac{x}{6}

6*tan(60)=x

x=6\sqrt{3}

So therefore we have solve for x, which is D) 6\sqrt{3}.

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Laura is creating the following design out of wood for it to be light enough she needs it’s area to be less than 80 square inche
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The area of a shape is the amount of space it can occupy.

<em>Laura's design will be light enough</em>

The shape is given as a trapezium (see attachment).

First, calculate the height (h) of the trapezium using the following Pythagoras theorem

5^2 = h^2 + x^2

Where:

x = \frac{11 - 9}{2} = 1

So, we have:

5^2 = h^2 + x^2

5^2 = h^2 + 1^2

25 = h^2 + 1

Collect like terms

h^2 = 25 -1

h^2 = 24

Take square roots

h = 4.90

The area of the shape is then calculated as follows:

Area = \frac{1}{2}(11  + 9) \times h

Area = \frac{1}{2}(11  + 9) \times 4.90

Area = \frac{1}{2} \times 20 \times 4.90

Area = 10 \times 4.90

Area = 49

The area of the shape is 49 square inches.

<em>Hence, the shape will be light enough (because 49 is less than 80)</em>

Read more about areas at:

brainly.com/question/16418397

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