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

Angle of elevation is 67.4
`\ degree`

Explanation:

Please refer the attached figure.

Given:- Height of Eiffel tower = 300 meter.

Distance of a point from the centre of the tower base = 125 meter.

To find:- Angle of elevation=?

Solution:-

Referring to attached figure, from the figure we can see that AB is the height of the Eiffel tower, BC is the point from the centre of the tower base and angle ACB is the angle of elevation.

Now, let angle of elevation = θ,

AB=300 m, and BC=125 m ------------------(1)

now in triangle ABC,

`tan\theta=(opposite)/(adjacent)`

`tan\theta=(300)/(125)`

`tan\theta=2.4`

`\theta=tan^(-1) (2.4)`

`\therefore\theta=67.38=67.4`

`\therefore\theta=67.4\ degree`

As θ is the angle of elevation,

Therefore angle of elevation is 67.4
`\ degree`