2 years ago

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

Mathematics

1 answer:

sammy [17]2 years ago

4 0

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Answer is 2

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the temperature outside was 50 during the day and fell 16 at night. What was the temperature at night?

mamaluj [8]

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The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of

Goryan [66]

ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

$\cos(60 \degree) = \frac{altitude}{hypotenuse}$

$\cos(60 \degree) = \frac{altitude}{8}$

Altitude =8cos(60°)

Altitude=4cm

Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

The upper radius meets the tangent at right angles.

From the smaller right triangle,

$\sin(60 \degree) = \frac{4 - y}{y}$

$y\sin(60 \degree) = 4 - y$

$y\sin(60 \degree) + y= 4$

$(\sin(60 \degree) + 1)y= 4$

$y= \frac{4}{\sin(60 \degree) + 1}$

$y = 16 - 8 \sqrt{3}$

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The length of a Diameter is 3.714

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