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Cos(x)=Adjacent/​Hypotenuse

(a) x=cos⁡^−1(Adjacent/Hypotenuse)​
(b) x=sin⁡^−1(Adjacent/Hypotenuse)
(c) x=tan⁡^−1(Adjacent/Hypotenuse)
(d) x=csc⁡^−1(Adjacent/Hypotenuse)

User Brillian
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1 Answer

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Final answer:

The correct trigonometric ratio for finding the angle x when given the adjacent side and hypotenuse of a right triangle is (a) x=cos⁻¹(Adjacent/Hypotenuse). This uses the inverse cosine function to calculate the angle.

Step-by-step explanation:

The correct answer to the given question is (a) x=cos⁻¹(Adjacent/Hypotenuse). This is because cos(x) is the trigonometric function that gives the ratio of the adjacent side to the hypotenuse in a right triangle. To find the angle x given the lengths of the adjacent side and the hypotenuse, we would use the inverse cosine function, which is commonly denoted as cos⁻¹ or arccos. So, if we know the adjacent side and hypotenuse, we can find the angle with x=cos⁻¹(Adjacent/Hypotenuse).

Other related concepts to this question include the Pythagorean theorem, which states x² + y² = h², and this can be used when finding the length of sides in a right triangle. Alongside these, we have trigonometric identities, such as sin 2θ = 2sinθcosθ and cos 2θ = cos²θ - sin²θ. These are useful for more advanced applications of trigonometry.

Moreover, we can use these trigonometric functions for calculating vector components in physics. The angle found by tan⁻¹(opposite/adjacent) gives the direction of the resultant vector when considering vectors in two dimensions.

User Shivam Pandya
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