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In a right triangle with one side measuring 7 units, a hypotenuse "x," and an angle of 25 degrees between the 7-unit side and the hypotenuse, what is the value of "x"?

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Final answer:

To calculate the hypotenuse 'x' in a right triangle with a 25-degree angle and an adjacent side of 7 units, use the cosine function (cos 25 degrees = 7 / x). Solving this equation provides the hypotenuse length, which is approximately 7.72 units.

Step-by-step explanation:

To find the value of the hypotenuse "x" in a right triangle where one side measures 7 units and there is a 25-degree angle between that side and the hypotenuse, we can use the cosine function from trigonometry. The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse (cos 25° = adjacent side / hypotenuse).

Since the side length of 7 units is adjacent to the 25-degree angle, we set up the following equation: cos 25° = 7 / x. We can solve for x by dividing 7 by the cosine of 25 degrees. To find the cosine of 25 degrees, we may use a calculator or trigonometric tables.

Using a calculator: cos 25° ≈ 0.9063, therefore x = 7 / 0.9063. After solving, we find that the hypotenuse, x, is approximately 7.72 units.

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