Virginia is flying a Cessna and is descending at a 9°9° angle towards a runway. If she can see a highway behind her at a 45°45° angle that is 300300 meters away from the runway, how much further does she have to fly until she lands? Round to the nearest tenth.
Question
Virginia is flying a Cessna and is descending at a 9°9° angle towards a runway. If she can see a highway behind her at a 45°45° angle that is 300300 meters away from the runway, how much further does she have to fly until she lands? Round to the nearest tenth.
Solution
To solve this problem, we can use trigonometry.
First, we need to understand that the situation described forms a right triangle. The runway is the base, the distance Virginia has to fly is the height, and the hypotenuse is the line from Virginia's current position to the highway.
We know the angle of descent (9°) and the length of the hypotenuse (300 meters). We want to find the height of the triangle, which is the distance Virginia has to fly.
We can use the sine of the angle of descent, which is equal to the opposite side (the height, or the distance Virginia has to fly) divided by the hypotenuse (300 meters).
So, sin(9°) = height / 300 meters.
To find the height, we rearrange the equation to: height = sin(9°) * 300 meters.
Using a calculator, sin(9°) is approximately 0.1564.
So, height = 0.1564 * 300 meters = 46.92 meters.
Rounding to the nearest tenth, Virginia has approximately 46.9 meters left to fly until she lands.
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