Mike and Lani stand 21.2 meters apart. From Mike’s position, the angle of elevation to the top of the Eiffel Tower is 40°. From Lani’s position, the angle of elevation to the top of the Eiffel Tower is 38.5°. How many meters high is the Eiffel Tower? Round to the nearest meter.

Answer 1

X1=Mike's distance from bottom of tower.
X1+21.2 = Lani's distance from bottom of
tower.

Tan40 = h/X1
h = X1*Tan40

Tan38.5 = h/(X1+21.2)
h = (X1+21.2)*Tan38.5

h = X1*Tan40 = (X1+21.2)*Tan38.5
0.839X1 = 0.795X1 + 16.86
0.044X1 = 16.86
X1 = 383 m.

h = 383 * Tan40 = 322 m.