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3 years ago

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.

cluponka [151]

<h3>How to determine the hypotenuse?</h3>

Step 1 and 2: Draw an isosceles right triangle

See attachment (figure 1) for this triangle

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

$h^2 = 1^2 + 1^2$

This gives

$h = \sqrt 2$

Step 4: Draw another isosceles right triangle

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

$h = \sqrt 5$

Step 5: Draw another isosceles right triangle

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

$h = \sqrt {10$

Step 6: Draw another isosceles right triangle

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