To measure the height of the cloud cover at an airport a wor

To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75 degree from the horizontal. An observer D = 550 m away measures the angle of elevation to the spot of light to be 45 degree. Find the height n of the cloud cover. m

Solution

There are two right angled triangles with height of h

Triangle1 : tan45 = h/x

h = x

Triagle 2 : tan75 = h/y

h = 3.732y ---> y = h/3.732

Now x +y = D = 550m

So, h + h/3.732 = 550

h (1.267) = 550

h = 434.09 = 434 mt