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Light Height is a puzzle in Professor Layton and the Last Specter.
Puzzle
- US Version
A single light hangs from a beam above the floor of this dilapidated warehouse.
There are two posts, both of which are a foot tall, separated by a distance of 15 feet. The light casts a 3 foot long shadow from the left post and a 2 foot long shadow from the right post.
Figure out how high the light is hanging above the floor.
- UK Version
A single light hangs from a high-up beam in this dilapidated warehouse. Down on the floor, there are two posts 1 m high and 15 m apart. The light casts a 3 m long shadow from the left post and a 2 m long shadow from the right.
How high, in metres, is the light from the floor?
Hints
Solution
Incorrect
- US Version
Too bad!
Your calculations aren't quite correct.
- UK Version
Bad luck!
Check your calculations and try again!
Correct
- US Version
That's right! The light is 4 feet tall!
As shown in the diagram, make two triangles, ABC and EBF, on the left of the light and two more, ADC and GDH, on the right.
AC:BC = EF:BF therefore
X:(Y+3) = 1:3
AC:CD = GH:HD therefore
X:(15-Y+2) = 1:2
Solving both of these equations will give you the value of X.
- UK Version
That's right! The light is 4 m up.
As shown in the diagram, make two triangles, ABC and EBF on the left of the light and two more, ADC and GDH, on the right.
AC : BC = EF : BF therefore
X : (Y + 3) = 1 : 3
AC : CD = GH : HD therefore
X : (15 - Y + 2) = 1 : 2
Using both these equations, you can work out the value of X.
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