Final answer:
The elevation increase on a hiking trail climbing at a 25º angle over a distance of 200 feet is found using the sine function, and it is approximately 84.52 feet, which is not one of the provided options.
Step-by-step explanation:
The question revolves around a hiking trail that climbs at a 25º angle. Given that a hiker travels a total linear distance of 200 feet along the trail, we want to find out how much their elevation has increased. To solve this problem, we can use the trigonometric function sine, as we are looking for the side opposite the angle in a right-angled triangle.
We have the angle (25º) and the hypotenuse (200 feet), and we are solving for the opposite side, which can be represented as follows in the equation involving the sine function:
sin(25º) = opposite / hypotenuse
Therefore:
opposite = sin(25º) × hypotenuse
opposite = sin(25º) × 200 feet
By calculating the sine of 25º and multiplying by 200, we can find the change in elevation. Using a calculator, we find that:
opposite ≈ sin(25º) × 200 feet ≈ 0.4226 × 200 feet ≈ 84.52 feet
Therefore, the elevation increase is approximately 84.52 feet, which means the correct answer is not listed in the multiple-choice options provided. It is important for the student to learn this approach so they can solve similar trigonometric problems in the future. Additionally, understanding the relationship between angles and side lengths in right-angled triangles is essential.