The airport meteorologists keep an eye on the weather to ensure the safety of the flights. One thing they watch is the cloud ceiling. The cloud ceiling is the lowest altitude at which solid cloud is visible. If the cloud ceiling is too low the planes are not allowed to take off or land.
One way a meteorologist can find the cloud ceiling at night is to shine a searchlight that is located a fixed distance from their office vertically into the clouds. Then they measure the angle of elevation to the spot of light on the cloud. The angle of elevation is the angle formed by the line of sight to the spot and the horizontal. Using trigonometry, the cloud ceiling can be determined.
Supposed a searchlight located 200 meters from a weather office is turned on. If the angle of elevation to the spot of light on the clouds is 350 , how high is the cloud ceiling?
Yes
To determine the height of the cloud ceiling, we can use trigonometry. Let's assume that the height of the cloud ceiling is represented by "h".
We have a right-angled triangle formed by the searchlight, the spot of light on the cloud, and the height of the cloud ceiling. The angle of elevation, 35°, is the angle between the horizontal and the line of sight to the spot.
Using the tangent function, we can set up the following equation:
tan(35°) = h/200
Now, we can solve for h by rearranging the equation:
h = 200 * tan(35°)
Calculating the value:
h ≈ 140.54 meters
Therefore, the cloud ceiling is approximately 140.54 meters high.
To determine the height of the cloud ceiling, we can use the concept of trigonometry.
Let's consider the situation:
- The searchlight is located 200 meters from the weather office.
- The angle of elevation to the spot of light on the clouds is 35 degrees.
We need to find the height of the cloud ceiling.
To solve this, we can use the tangent function. The equation for tangent is given by:
tan(angle) = opposite / adjacent
In this case, the angle of elevation to the spot of light is 35 degrees, and the adjacent side is the horizontal distance between the searchlight and the weather office, which is 200 meters. The opposite side is the height of the cloud ceiling, which we need to calculate.
Using the tangent function, we can rearrange the equation:
tan(angle) = opposite / adjacent
tan(35) = height / 200
To solve for the height, we can multiply both sides by 200:
height = 200 * tan(35)
Using a calculator, we can calculate this value:
height ≈ 200 * 0.7 ≈ 140 meters
Therefore, the height of the cloud ceiling is approximately 140 meters.
The angle of elevation is 350 ???
I suspect a typo.
Did you mean 35° ?
Correct your typo, then set it up like I showed you in the previous post.