the distance two stakes on a slope is taped at 2055 feet and the angle of the slope with the horizontal is 12.3 degrees. find the horizontal distance between the stakes
That distance x can be found using
cos12.3° = x/2055
To find the horizontal distance between the stakes, we need to use some trigonometry. In this case, we can use the sine function to calculate the horizontal distance.
The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse. In this problem, the hypotenuse is the distance between the stakes (2055 feet), and the opposite side is the vertical distance.
To find the vertical distance, we can use the sine function:
sin(angle) = opposite / hypotenuse
Rearranging the equation, we get:
opposite = sin(angle) * hypotenuse
Now we can substitute the given values:
opposite = sin(12.3 degrees) * 2055 feet
Using a calculator, we find that sin(12.3 degrees) is approximately 0.2113.
opposite = 0.2113 * 2055 feet
≈ 434.6035 feet
So, the vertical distance between the stakes is approximately 434.6035 feet.
To find the horizontal distance, we need to use the cosine function. The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. In our case, the adjacent side is the horizontal distance we want to calculate.
cosine(angle) = adjacent / hypotenuse
Rearranging the equation, we get:
adjacent = cosine(angle) * hypotenuse
Using the given values, we have:
adjacent = cos(12.3 degrees) * 2055 feet
Using a calculator, we find that cos(12.3 degrees) is approximately 0.9772.
adjacent = 0.9772 * 2055 feet
≈ 2009.196 feet
Therefore, the horizontal distance between the stakes is approximately 2009.196 feet.