### INTRODUCTORY EXERCISES-Modelling with Trigonometric Functions

**(3)** The angle of elevation to the top of the Empire State Building in New York is found to be 11^{o} from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the Empire State Building.

**SOLUTION:**

opposite side
tan = ---------------
adjacent side
x
tan 11^{o} = --- = x
1
tan 11^{o} = 0.1944
Therefore,
x = 0.1944 miles
(Recalling that there are 5280 feet/mile,
0.1944 miles*5280 feet/mile = approximately 1026 feet)

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