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vekshin1
3 years ago
14

What is the value of x in the diagram below?

Mathematics
1 answer:
otez555 [7]3 years ago
8 0

The cosine of 30° is √3 / 2.

Since cosine is Adjacent over Hypotenuse, Hypotenuse = (2 / √3) * 9 = 18 / √3.

The cosine of 45° is √2 / 2.

Therefore, X = (2 / √2) * (18 / √3) = 36 / √6 = 18 / √1.5 = C

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Step 1: Place the graph paper in landscape orientation. Measure from the top left hand corner 6 inches right and 5 inches down.
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<h3>How to determine the hypotenuse?</h3>

<u>Step 1 and 2: Draw an isosceles right triangle</u>

See attachment (figure 1) for this triangle

The legs of this triangle have a length of 1 inch

<u>Step 3: The hypotenuse</u>

This is calculated using the following Pythagoras theorem

h^2 = 1^2 + 1^2

This gives

h = \sqrt 2

<u>Step 4: Draw another isosceles right triangle</u>

Add 1 inch to one of the legs

See attachment (figure 2) for this triangle

The legs of this triangle have lengths of 1 inch and 2 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

h^2 = 2^2 + 1^2

This gives

h = \sqrt 5

<u>Step 5: Draw another isosceles right triangle</u>

Add 1 inch to one of the legs

See attachment (figure 3) for this triangle

The legs of this triangle have lengths of 1 inch and 3 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

h^2 = 3^2 + 1^2

This gives

h = \sqrt {10

<u>Step 6: Draw another isosceles right triangle</u>

Add 1 inch to one of the legs

See attachment (figure 4) for this triangle

The legs of this triangle have lengths of 1 inch and 4 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

h^2 = 4^2 + 1^2

This gives

h = \sqrt{[17

See that the hypotenuse is the square root of 17

Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17

Read more about right triangles at:

brainly.com/question/2437195

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