Liola drives 13 km up a hill that is at a grade of 10 Degrees what horizontal distance to the nearest tenth of kilometer has she covered
X = 13km * cos10 = 12.8 km.
To find the horizontal distance Liola has covered, we need to use trigonometry. The grade of the hill is given as 10 degrees, which means the angle between the hill and the horizontal ground is 10 degrees.
We can use the sine function to calculate the horizontal distance:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the horizontal distance we are looking for, and the hypotenuse is the distance Liola drives up the hill (13 km). Rearranging the formula, we have:
horizontal distance = sin(angle) x hypotenuse
Substituting the given values into the formula:
horizontal distance = sin(10 degrees) x 13 km
Using a calculator to find sin(10 degrees) ≈ 0.1745, we can calculate the horizontal distance:
horizontal distance ≈ 0.1745 x 13 km
horizontal distance ≈ 2.2675 km
Therefore, Liola has covered a horizontal distance of approximately 2.3 km to the nearest tenth of a kilometer.
To determine the horizontal distance Liola has covered, we need to find the value of the adjacent side of the right triangle formed by the hill and the horizontal ground.
In this case, the hypotenuse of the triangle is the distance Liola drives up the hill, which is 13 km. The angle of the incline is 10 degrees.
To find the adjacent side (horizontal distance), we can use the cosine trigonometric function. The formula is:
adjacent side = hypotenuse * cosine(angle)
Using this formula, we can substitute the given values:
adjacent side = 13 km * cosine(10 degrees)
Now, let's calculate the horizontal distance to the nearest tenth of a kilometer.
cosine(10 degrees) ≈ 0.9848 (rounded to four decimal places)
adjacent side ≈ 13 km * 0.9848
adjacent side ≈ 12.8036 km
Therefore, Liola has covered a horizontal distance of approximately 12.8 kilometers to the nearest tenth of a kilometer.