Question

The eiffel tower in paris is 300 meters high (not including the antenna on top). What is the angle of elevation of the top of the tower from a point on the ground (assumed level) that is 125 meters from the centre of the tower's base?

The answer in my textbook says 67.4 but I dont know how they got there

Answer 1

The answer to your question is 67.3°

Explanation:

Data

height = 300 m = opposite side

base = 125 m = adjacent side

angle = Ф = ?

Process

1.- From the data given and the explanation, we can imagine that we are working with a right triangle. And the lengths correspond to the legs of this triangle.

2.- Look for a trigonometric function that relates the opposite side and the adjacent side.

This trigonometric function is tangent.

tan Ф =
`(Opposite side)/(Adjacent side)`

3.- Substitution

tan Ф =
`(300)/(125)`

4.- Simplify

tan Ф = 2.4

5.- Find the angle (tan⁻¹Ф)

tan⁻¹ 2.4 = 67.3°