Answer: [tex]75.96^{\circ}[/tex].
Step-by-step explanation:
By considering the given information we draw a picture to represent the situation ( given in attachment)
Since the tower stands vertical to the ground , therefore , the triangle is a right triangle.
Let x be the angle of elevation from a point 50 feet from the base of the tower to the top of tower.
According to the trigonometry , the tangent of an angle is the ratio of "the side opposite to angle" to "the side adjacent to the angle".
For the triangle below , [tex]\tan x=\dfrac{200}{50}=4\\\\ x=\tan^{-1}(4)=1.32581766\ radians\ [\text{By scientific calculator}]\\\\=1.32581766\times\dfrac{180^{\circ}}{\pi}\ \\\\=75.9637563^{\circ}=75.96^{\circ}[/tex]
[Note:To convert radians into degrees we multiply it by [tex]180^{\circ}}[/tex] and divide it by[tex]\pi[/tex]]
Hence, the angle of elevation from a point 50 feet from the base of the tower to the top of tower is [tex]75.96^{\circ}[/tex].
