Answer:
45° is the angle of elevation
Explanation:
A picture speaks a 1000 words. See the attached diagram
AB represents the man 1.75m
AC as well as BE represents the horizontal distance from the man to the tower which is given 50m
BD is the line of sight from the man's eyes to the top of the tower
The relative height of the tower from the man's eyes to the top of the tower = 51.75 - 1.75 = 50m
The angle of elevation is the angle ∠DEB of triangle ΔDBE
We can compute ∠DEB in two ways
1. By noting that ΔDBE is a right isosceles triangle
Since BE = ED.
∠DBE= ∠BDE
∠DEB = 90° (right triangle)
So ∠DBE+ ∠BDE = 180 -90 = 90° (sum of angles adds up to 180)
2∠DBE = 90
∠DBE = 45°
2. By trigonometry
Since ΔDBE is a right triangle, we can determine m∠DEB using the formula using
tan(∠DBE) = DE/BE
Since DE = BE = 50,
DE/BE = 1
So tan(∠DBE) = 1
∠DBE = tan⁻¹ (1) = 45°