Question

FAN + MEDAL



A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B and C, as shown below:


What is the distance between the walls?

Answer 1

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Answer 2

To solve AB:
\[\sin(60) = \frac{ opposite }{ hypotenuse }\]
\[\sin(60) = \frac{ 60 }{ x }\]
Make x the subject of the formula
\[x = \frac{ 60 }{ \sin(60) }\]
And then solve
\[x = \frac{ 60 }{ \frac{ \sqrt{3} }{ 2 } }\]
\[x = \frac{ 60 \times 2 }{ \sqrt{3} }\]
\[x = \frac{ 120 }{ \sqrt{3} }\]
\[x = \frac{ 120 }{ \sqrt{3} }\]\[x = 40\sqrt{3}\]\[x = 69.28m\]
And then for AC you do the exact same thing, just substitute different values in

Answer 3

Then you work out the size of the unknown part of A
\[180 = 60 + 30 + A\]\[A = 90\]
And as A = 90, you can use Pythagoras to work out the distance between the two walls
\[a ^{2} + b ^{2} = c ^{2}\]\[AB ^{2} + AC ^{2} = BC ^{2}\]

Answer 4

@imamod Does this solve your problem?