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Alyosha and Ivan are standing between two buildings they know to be equal height. The buildings are 500 feet apart. Looking up at the westernmost building, they form a 30 degree angle. Looking to the northeastern building, they form a 45 degree angle.

A) Ivan guesses they are halfway between the buildings. Why is this a bad guess?

B) How far away from each building are they?

Alyosha and Ivan are standing between two buildings they know to be equal height The buildings are 500 feet apart Looking up at the westernmost building they fo class=

Respuesta :

Refer to the diagram shown below.

h = height of each building
x =  distance from the left building
y =  distance from the right building

Because the distance between the buildings is 500 feet, therefore
x + y = 500    (1)

By definition,
tan 45° = h/y = 1
y = h             (2)

Also,
tan 30° = h/x = 1/√3
x = h√3        (3)

Part (a)
If Alyosha and Ivan were halfway between the building, then x = y.
Because x ≠ y, they are not halfway between the buildings.

Part (b)
From (1), (2) and (3), obtain
h + h√3 = 500
h(1+√3) = 500
2.732h = 500
h = 183.0 ft

Therefore
x = 183.0 ft
y = 500 - x = 317.0 ft

Answer:
Alyosha and Ivan are 183 feet from the left building, and 317 feet from the right building.
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