Answer:
Given the statement: For a person standing 100 m from the center of the base of the excel tower, the angle of elevation to the top of the tower is 71.6 degrees.
Let h be the height of the Eiffel tower.
Angle of elevation is, [tex]\theta =71.6^{\circ}[/tex]
Distance of boy standing from the center of the base of the Eiffel tower is, 100 m.
Using tangent ratio:
[tex]\tan \theta = \frac{\text{opposite side}}{\text{Adjacent side}}[/tex]
From the given figure as shown;
Solve for h;
[tex]\tan 71.6 = \frac{h}{100}[/tex]
Multiply both sides by 100 we have;
[tex]h = 100 \tan 71.6[/tex]
or
[tex]h = 100 \times 3.0061109035[/tex]
Simplify:
[tex]h \approx 300 m[/tex]
therefore, the height of the Eiffel tower is, 300m
