Question

A tower is 200 feet tall. To the nearest degree, find the angle of elevatio n from a point 50 feet from the base of the tower to the top of tower.

Answer 1

Answer: $75.96^{\circ}$.

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 , $\tan x=\dfrac{200}{50}=4\\\\ x=\tan^{-1}(4)=1.32581766\ radians\ [\text{By scientific calculator}]\\\\=1.32581766\times\dfrac{180^{\circ}}{\pi}\ \\\\=75.9637563^{\circ}=75.96^{\circ}$

[Note:To convert radians into degrees we multiply it by $180^{\circ}}$ and divide it by$\pi$]

Hence, the angle of elevation from a point 50 feet from the base of the tower to the top of tower is $75.96^{\circ}$.