Answer:
Height of the cloud ceiling in feet = 6500 feet.
Step-by-step explanation:
i) the searchlight will form a right angled triangle and the base of the triangle is the distance of the searchlight from the weather station.
ii) let us say that the angle of elevation, Θ = 45°.
Therefore from the formulas used for a right angled triangle we can say that [tex]tan(\theta) = \frac{opposite}{adjacent} = \frac{height}{base}[/tex] which gives [tex]tan(\theta) = tan(45\textdegree) = 1 = \frac{height}{base} = \frac{height}{6500 feet}[/tex]
therefore height = 6500 feet.
The cloud ceiling is 6500 feet high from weather station.
A diagram is attached below,
In figure, A represent search light and C represent cloud ceiling.
Let us consider that height of cloud ceiling from weather station is h.
Apply tan function of angle in right triangle,
[tex]tan(45)=\frac{h}{6500}\\ \\ 1=\frac{h}{6500} \\ \\ h=6500feet[/tex]
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