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Citrus2011 [14]
1 year ago
12

an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highwa

y on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?
Mathematics
1 answer:
rosijanka [135]1 year ago
6 0

The first and second cars are 7724 feet apart from each other.

The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:

     tan = opposite/ adjacent

⇒  tan(31°) = 3500/x

⇒ 0.60086 = 3500/x

⇒ 0.67 x = 3500            [ rounding up 0.60086 = 0.67]

⇒ x = 5223.88

That means the first car is 5223.88 feet from the point on the highway below the plane.

We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:

    tan(53°) = 3500/x

⇒ 1.327 = 3500/x

⇒ 1.4x = 3500            [ rounding 1.327 = 1.4]

⇒ x = 3500/1.4
⇒ x = 2500

That means the second car is 2500 feet from the point on the highway below the plane.

Add the two distances together to get the total distance from car to car:

5223.88 + 2500.00 = 7723.88

So, rounded to the nearest foot, the cars are 7724 feet apart.

Learn more about Vertex:

brainly.com/question/29030495

#SPJ4

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