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12) To ensure the safety of the flights, airportmeteorologists have to determine is cloud ceiling. Thecloud ceiling is the lowest altitude at which solid cloud isvisible. If the cloud ceiling is too low the planes are notallowed to take off or land.One way a meteorologist can find the cloud ceiling atnight is to shine a searchlight that is located a fixeddistance from their office vertically into the clouds. Thenthey measure the angle of elevation, with a clinometer, tothe spot of light on the cloud. Using trigonometry, thecloud ceiling can be determined.A searchlight located 200 meters from aweather office is turned on. If the angle ofelevation to the spot of light on the cloudsis 35º, how high is the cloud ceiling?©2014 19 joan kessler distancemath.com

Sagot :

Answer:

The cloud ceiling is 140 meters high

Explanations:

Let the height of the cloud ceiling be h

The distance of the searchlight to the weather office = 200 m

The angle of elevation, θ = 35º

The diagram below represents the given illustration

From the diagram shown ablove:

[tex]\begin{gathered} \tan \text{ }\theta\text{ = }\frac{Opposite}{\text{Adjacent}} \\ \tan \text{ 35 = }\frac{h}{200} \\ h\text{ = 200 }\tan \text{ 35} \\ h\text{ = 200 (}0.7) \\ h\text{ = }140\text{ m} \end{gathered}[/tex]

The cloud ceiling is 140 meters high

View image TywoneG749066
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