# Geometry

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.

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3. 👁 400
1. A = 180-40 = 140o.
B = 180-40-38.5 = 1.5o, b = 21.2 m.
C = 38.5o.

Using Law of sines:
a/sinA = b/sinB
a/sin140 = 21.2/sin1.5.
Multiply both sides by sin140:
a = 21.2*sin140/sin1.5 = 520.6 m.

h = a*sinC = 520.6*sin38.5 = 324 m.

We drew 2 rt triangles with a common ver. side, h. Line BC was drawn from top
of Bldg to the end of a hor line to form
hyp. of the larger triangle. Line BA was
drawn from top of Bldg to a point on hor. line to form hyp. of smaller triangle. AB = 21.2 m.

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posted by Henry
2. post it.

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posted by Henry
3. h

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2. 👎 0

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