Question

A searchlight is 6500 feet from a weather station. If the angle of elevation to the spot of light on the clouds above the station is 45°, how high is the cloud ceiling in feet?

Answer 1

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 $tan(\theta) = \frac{opposite}{adjacent} = \frac{height}{base}$ which gives $tan(\theta) = tan(45\textdegree) = 1 = \frac{height}{base} = \frac{height}{6500 feet}$

 therefore height = 6500 feet.