An airplane is at an altitude of 10 km. You spot the

airplane at an angle of 55 degrees . How far away
Is the airplane directly from you? Give your answer to the nearest kilometre.

better start reviewing the trig functions.

10/x = sin 55

To find the distance to the airplane directly from you, we can use trigonometry.

Let's assume that you are standing on the ground and looking up at the airplane. The given angle of 55 degrees can be considered as the angle of elevation from your eye level to the airplane.

Now, we can use the tangent function, which relates the opposite side (the altitude of the airplane) to the adjacent side (the distance from you to the airplane).

Tangent of an angle = opposite/adjacent

In this case, the opposite side is the altitude of the airplane (10 km), and the angle is 55 degrees. We need to find the adjacent side, which is the distance from you to the airplane.

So, we can rearrange the equation to solve for the adjacent side:

Adjacent = opposite / tangent(angle)

Adjacent = 10 km / tan(55 degrees)

Now, we can plug this into a calculator to find the value of tangent(55 degrees) and calculate the distance:

Adjacent ≈ 10 km / tan(55 degrees) ≈ 10 km / 1.428 ≈ 7.00 km.

Hence, the airplane is approximately 7 kilometres away from you directly.