52. Liola drives 19 km up a hill that is at a grade of 15o. What horizontal distance, to the nearest tenth of kilometer, has she covered?
a.5.1 km
b.4.9 km
c.14.2 km
d.18.4 km
cosA = x/r
cos 15 = x/19
X = 18.4 km.
To find the horizontal distance covered by Liola, we can use trigonometry.
The horizontal distance (d) can be calculated using the equation:
d = distance travelled * cosine(angle)
Given that Liola drives 19 km up a hill at a grade of 15o, we can substitute the values into the equation:
d = 19 km * cosine(15o)
Using a calculator, we can find the value of cosine(15o) to be approximately 0.9659.
d ≈ 19 km * 0.9659
d ≈ 18.3431 km
Therefore, the horizontal distance covered by Liola, to the nearest tenth of a kilometer, is approximately 18.3 km.
So, the correct answer is option d. 18.4 km.
To find the horizontal distance covered by Liola, we can use trigonometry.
Since we are given the distance Liola drives up the hill and the grade of the hill, we can use the sine function to find the horizontal distance.
The sine function relates the opposite side (in this case, the vertical distance) to the hypotenuse (the longest side of the right triangle formed). In this case, the hypotenuse is the distance Liola drives up the hill, and the opposite side is the vertical distance.
Using the formula sin(angle) = opposite/hypotenuse, we can rearrange it to solve for the opposite side:
opposite = sin(angle) * hypotenuse
In this case, the angle is 15 degrees and the hypotenuse (distance up the hill) is 19 km. Plugging in the values:
opposite = sin(15) * 19
Calculating this expression:
opposite = 0.2588 * 19
opposite = 4.9092 km
Therefore, Liola has covered approximately 4.9 km horizontally.
So the correct answer choice is b. 4.9 km.