In making a topographical map, it is not practical to measure directly heights of structures such as mountains. This exercise illustrates how some such measurements are taken. A surveyor whose eye is a = 7 feet above the ground views a mountain peak that is c = 4 horizontal miles distant. (See the figure below.) Directly in his line of sight is the top of a surveying pole that is 10 horizontal feet distant and b = 8 feet high. How tall is the mountain peak? Note: One mile is 5280
eet.
+37146 Using similar triangles:
1 ft / 10 ft = x ft / (5280 x 4)ft x = 2112 PLUS the 7 ft observer's 'eye-height' = 2119 ft high mountain
Using trig fxns:
For the surveyor's pole:
Tan theta = 1/10 theta = 5.71 degrees
For the mtn:
tan 5.71 = opp/adj = opp/(4 x 5280 ft) opp = 2112 2112 + observer's height (7 ft .....very tall surveyor) = 2119 ft high
