Solve the problem.
-A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed, the angle of depression to the car is 45° 56´. When the car
Stops, the angle of depression is 22° 34´. The building is 270 feet tall. How far did the car travel from
When it was first noticed until it stopped? Round to the nearest foot.
A)415 ft
B)588 ft
C)367 ft
D)388 ft

Question

Quizplus · Accepted Answer

The distance the car traveled can be found by calculating the difference in the horizontal distances from the building at the two angles of depression. Using the tangent of an angle in a right triangle (tan(θ) = opposite/adjacent), where the opposite side is the height of the building (270 feet) and the adjacent side is the distance from the building to the car, we can find the distances for both angles.For the first angle of depression (45° 56´), we approximate it to 46° for calculation purposes. The tangent of 46° is approximately 1, which means the distance from the building when the car was first noticed is approximately equal to the height of the building, 270 feet.For the second angle of depression (22° 34´), we use the tangent of 22.5667° (approximating 34 minutes to its decimal equivalent). The tangent of 22.5667° is approximately 0.414. So, the equation to find the distance when the car stopped is 270 / 0.414 ≈ 652 feet.The car traveled the difference between these two distances: 652 feet - 270 feet = 382 feet. Since the answer must be rounded to the nearest foot and none of the provided choices exactly match this calculation, the closest provided option is 388 feet, acknowledging a possible slight variation in the exact trigonometric values used or rounding during calculation steps.

Solve the Problem. -A Person Is Watching a Car from the Top of the Top