Question

In aviation, it is helpful for pilots to know the cloud ceiling, which is the distance between the ground and lowest cloud. The simplest way to measure this is by using a spotlight to shine a beam of light up at the clouds and measuring the angle between the ground and where the beam hits the clouds. If the spotlight on the ground is 0. 75 km from the hangar door as shown in the image below, what is the cloud ceiling?.

Answer 1

Unfortunately, I cannot see the image you are referring to. However, I can provide the general formula for calculating the cloud ceiling using the method you described.

To calculate the cloud ceiling, you need to measure the angle between the ground and where the beam of light hits the clouds, and you also need to know the distance between the spotlight and the point on the ground directly below where the beam hits the clouds. Let's call this distance "d", and let's call the angle between the ground and the beam of light "θ".

Then, the cloud ceiling can be calculated using the tan function:

tan(θ) = cloud ceiling / d

Solving for the cloud ceiling, we get:

cloud ceiling = d * tan(θ)

In your specific case, if the spotlight is 0.75 km from the hangar door, then you need to measure the angle θ between the ground and where the beam of light hits the clouds, and you need to measure the distance "d" between the spotlight and the point on the ground directly below where the beam hits the clouds.

Once you have these measurements, you can use the formula above to calculate the cloud ceiling. Remember to use consistent units for all measurements (for example, kilometers for distance and degrees for angles).

Step-by-step explanation: