Trigonometry, exemplified through the sine function, accurately determines the length x (487) in a right triangle with a 70-degree angle and hypotenuse h = 520, showcasing practical math in problem-solving.
To find the length x in a right triangle, trigonometry can be used, focusing on the sine function. In this context, let h be the hypotenuse and a be the angle opposite side x. The sine of angle a is defined as the ratio of x to h, expressed as sin(a) = x/h.
For a specific scenario where a = 70 degrees and h = 520, the equation can be rearranged to solve for x: x = h * sin(a). Substituting the given values, x = 520 * sin(70), and after computation, x is approximately 487. Rounding to the nearest whole number, the length x is 487.
This trigonometric method provides an accurate means of determining x in a right triangle, showcasing the practical application of mathematical principles in real-world problem-solving.