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Ignoring an error (Posted on 2018-08-30) Difficulty: 2 of 5
During a math exam, one of the students erroneously copied a trig problem, the original being:
In a triangle ABC, AB=9 cm, AC="...", and the angle BAC=60 deg.
Find the length of side BC.

"..." provided a number which the student copied, increasing it by 1 cm.
Still he got the correct answer.

What was it?

No Solution Yet Submitted by Ady TZIDON    
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Solution solution Comment 2 of 2 |
Consider vertex A (the 60° angle) at the left end of the base and B at the apex of the triangle. Drop a perpendicular from B forming a right angle at D, on AC. D is 4.5 units from A, so the two answers that both happen to be correct have point C either 4 units from A or 5 units.

Both lengths do give the same answer when using the law of cosines:

x^2 = 81 + 16 - 72*1/2
    = 97 - 36
    = 61
x = sqrt(61)

x^2 = 81 + 25 - 90*1/2
    = 106 - 45
    = 61
x = sqrt(61)  

That's about  7.810249675906654

Edited on August 30, 2018, 2:40 pm
  Posted by Charlie on 2018-08-30 14:31:32

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