Problem Schematic

As shown in the figure, the height of the tree can be determined as follows:

     tan(π/9) = 75/h
     h = 75cos(π/9)/sin(π/9)

Without a scientific calculator which has trigonometric functions, one can approximate the sine and cosine functions using Taylor series:

     

For the present case study, only three terms are retained for the approximation. For x = π/9,

The height of the tree is then given by:

     h = 75(0.940)/(0.342) = 206 ft

Hence, this is not the tallest tree. It is not even close to the height of the tallest redwood, which is around 370 feet.

(Note: For comparison purposes, determine the sine and cosine functions using a scientific calculator and see if the approximation given above is close enough.)