1. To avoid a steep descent, an airplane flying at 10 000 m starts its descent 60km away from the airport. For the angle of descent to be constant, at what angle should the plane descend?
2. A flagpole that is 20m high casts a shadow that is 18m long. What is the angle of elevation from the ground to the top of the flagpole?
1. The first thing you need to do is convert 60km to meters, or 10,000m to kilometers; whichever you prefer. Next,it helps if you draw a right triangle. The plane is at a height of 10,000m; this is the vertical leg of the triangle. It is 60 km away from the airport; this is the horizontal leg of the triangle. The question is asking for the angle of descent; this is the angle(I'm going to call it <A) between the hypotenuse and the vertical leg. Since you have the lengths of the horizontal and vertical legs, you're going to have to use the Pythagorean theorem to find the length of the hypotenuse. Once you do, you can use either cosine of <A (which is the vertical leg-10,000m-divided by the hypotenuse) or sin(<A), (which is the horizontal leg-60km- divided by the hypotenuse), to find your answer. You can plug that into a calculator; don't forget to put your calculator in degree mode, to get the angle in degrees.
2. You'll need to draw another right triangle. The vertical leg is 20m; the horizontal leg is 18m. The angle of elevation is the angle (I'm going to call it <B) between the horizontal leg and the hypotenuse. Use Pythagorean theorem to find the hypotenuse, then find the angle of elevation by doing either cos(<B) or sin(<B).
Thanks much :)
To answer these questions, we can use trigonometry. Specifically, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side in a right triangle.
Let's break down each question step by step:
1. To find the angle of descent, we need to determine the ratio of the altitude change to the horizontal distance covered. In this case, the altitude change is 10,000m, and the horizontal distance covered is 60km (which is equal to 60,000m).
So, we have:
tangent(angle) = 10,000m / 60,000m
angle = arctan(10,000m / 60,000m)
To find the value, we can input this equation into a scientific calculator or use an online trigonometric calculator to get the result.
2. To find the angle of elevation, we need to determine the ratio of the height of the flagpole to the length of its shadow. In this case, the height of the flagpole is 20m, and the length of the shadow is 18m.
So, we have:
tangent(angle) = 20m / 18m
angle = arctan(20m / 18m)
Again, we can input this equation into a scientific calculator or use an online trigonometric calculator to find the result.
Remember to use the "arctan" or inverse tangent function to obtain the angle since we are finding the angle based on a ratio.