We can use the cosine trigonometric ratio here to find the height of Eiffel Tower.
The height of Eiffel Tower is found as 1063.96 feet approximately.
Given that:
- Mai is 80 feet away from the tower.
- She is looking up the tower's top at an angle of 85.7 degrees.
To find:
The height of Tower
Using the right angled triangle's cosine ratio from angle of elevation:
Refer to the diagram attached below.
Assuming height of Mai is negligible in comparison to height of Eiffel tower, we have triangle ABC as right angled triangle.
Using cosine of angle C (since we're given base length and length of perpendicular is needed which is height of tower), we get:
[tex]tan(C) = \dfrac{AB}{BC}\\\\
tan(85.7^\circ) = \dfrac{h}{80}\\\\
h = tan(85.7^\circ) \times 80\\
h \approx 13.2995 \times 80\\
h \approx 1063.96 \: \rm feet[/tex]
Thus, height of the Eiffel tower is found to be 1063.96 feet approximately.
Learn more about trigonometric ratio and height related problems here:
https://brainly.com/question/15635633
