Answer :
Final answer:
To find the altitude using the slope of 1500 meters and a slope angle of 45 degrees, trigonometry is used, yielding an elevation gain of approximately 1060.65 meters, which is closest to option (a) 1066.67 meters.
Explanation:
To find the altitude of the hill (the vertical height above the starting elevation), known as the elevation gain, we can apply trigonometric principles. Given the slope (hypotenuse) is 1500 meters and the elevation from the ground (opposite side) is 45 meters, we can use the sine function as follows:
Step 1: Identify the relevant ratio
Since we know the slope distance (hypotenuse) and the angle of elevation, we will use the sine function which relates the angle to the ratio of the opposite side to the hypotenuse.
Step 2: Apply the sine function
The sine of the elevation angle is equal to the opposite side (elevation gain) divided by the hypotenuse (slope distance).
sin(Θ) = opposite / hypotenuse
Step 3: Solve for the opposite side (elevation gain)
Let's assume the typo that states the elevation from the ground is 45, is actually meant to indicate an angle of 45 degrees. Therefore:
sin(45°) = elevation gain / 1500 m
elevation gain = 1500 m * sin(45°)
elevation gain = 1500 m * 0.7071 (approximate value of sin(45°))
elevation gain = 1060.65 meters (approximate)
The closest answer from the provided options would be (a) 1066.67 meters.
