Viola drives 200 meters up a hill maing a 9 degree angle with the horrizontal. What horizontal distanmce has she cover. To the nearest tenth meter.
1,262.8m
200.4m
197.5m
31.3m***
No. You calculated 200 sin9° but you want cos9°
Always do a sanity check. 9° is a very slight slope. The horizontal distance is almost the same as the distance along the hill.
Thank you
So it would be 197.5
yes
To find the horizontal distance that Viola has covered, we can use trigonometry and the given information about the angle and the vertical distance.
We are given that the angle between the hill and the horizontal is 9 degrees, and the vertical distance that Viola covers is 200 meters. We want to find the horizontal distance.
To find the horizontal distance, we can use the trigonometric function tangent (tan). The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the vertical distance of 200 meters, and the adjacent side is the horizontal distance that we want to find.
So, we can use the formula: tan(angle) = opposite/adjacent.
tan(9 degrees) = 200/adjacent
Now, we can solve for the adjacent side (the horizontal distance) by rearranging the equation:
adjacent = 200 / tan(9 degrees)
Using a calculator, we find the value of tangent (tan) of 9 degrees is approximately 0.15838444.
adjacent = 200 / 0.15838444
adjacent ≈ 1262.78
So, the horizontal distance that Viola has covered is approximately 1262.78 meters.
Therefore, the answer is 1,262.8m (to the nearest tenth meter).