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Let 
be an integer. Suppose there is a triangle with legs of length 16 and 
. Then by the Pythagorean theorem, the length of the hypotenuse should be
The formulas for Pythagorean triples say that if the legs are integers, then so must be the hypotenuse, because if
and 
are integers, then so are 
, 
, and 
.
However,
is not a perfect square trinomial, which means for any integer , the length of the hypotenuse is not an integer, so such a triangle doesn't exist.
The formulas for Pythagorean triples say that if the legs are integers, then so must be the hypotenuse, because if
However,
Height of the tower = 101.9 m
Solution:
Given data:
Angle θ = 27°
Adjacent side = 200 m
Opposite side = Height
Let height be taken as h.
The given image shows it is a right triangle.
Using basic trigonometric ratio formulas,
The value of tan 27° = 0.5095
Do cross multiplication, we get
0.5095 × 200 = h
101.9 = h
Height of the tower = 101.9 m