Question 220757
The U.S. Weather Bureau defines a cloud ceiling as the altitude of the lowest clouds that cover more than half the sky. 
To determine a cloud ceiling, a powerful searchlight projects a circle of light vertically on the bottom of the cloud.
 An observer sights the circle of light in the crosshairs of a tube called a clinometer. 
A pendant hanging vertically from the tube and resting on a protractor gives the angle of elevation. 
Find the cloud ceiling if the searchlight is located 1000 feet from the observer and the angle of elevation is 30.0° as measured with a clinometer at eye-height 6 feet.
 (Assume three significant digits.)
Please help solve and explain this.
:
this is a right triangle, one leg is 1000 ft, the other leg is the elevation you are looking for.
Use the tangent of 30 degrees, {{{(side opposite(h))/(side adjacent(1000))}}}
tan(30) = {{{h/1000}}}
h = 1000(.577345)
h = 577.350 ft
:
However since this triangle is at eye level (6'), elevation will be
577.35 + 6 = 583.35 ft