Final answer:
Using trigonometry with the given angle of depression of 8° and a height of 38 meters, neither of the options provided matches the calculated straight-line distance from Angie to her car. An error might exist either in the options or in the angle provided.
Step-by-step explanation:
To calculate the straight-line distance from Angie to her car, we must use trigonometry. Since Angie is 38 meters above the ground and the angle of depression from her to the car is 8°, we can represent this situation with a right triangle where the height is 38 meters and the angle from the balloon to the car is the angle of depression. We are interested in finding the length of the hypotenuse.
The angle of elevation from the car to Angie would also be 8° due to alternate interior angles created by a horizontal line from Angie's position and the line of sight to the car. We can use the tangent function, which is defined as the opposite side over the adjacent side in a right-angled triangle:
tan(8°) = opposite / adjacent
The 'opposite' side is the height, which is 38 meters. Let's call the 'adjacent' side 'd', which is the horizontal distance from the car to the point directly under the hot air balloon.
tan(8°) = 38 / d
Now we can solve for 'd':
d = 38 / tan(8°)
To find the hypotenuse (the straight-line distance), we use the Pythagorean theorem. However, we can also directly use the cosine function provided we are looking for the hypotenuse:
cos(8°) = d / hypotenuse
We can now solve for the hypotenuse:
hypotenuse = d / cos(8°)
Upon calculation, you will find that none of the given options (a) 38 meters, (b) 76 meters, (c) 285 meters, (d) 2850 meters match the correct value. Therefore, there might be an error in the options provided, or there may have been a typo in the given angle of depression.