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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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student's luck (solved?) | Comment 1 of 2

I get  BC~7.81 cm.

Method: I made the base AC and imagined angle ACB to be slightly great than 90 deg. I then extended the base to erroneous point C', 1 cm further out. Since BC=BC', triangle BCC' is isosceles. I dropped a perpendicular from B to the base, which I called D which is halfway between C and C'.   CD = C'D = 0.5 cm.

Now, BD = 9 sin 60 = 9 sqrt(3)/2. The similar right triangles BDC and BDC' have sides 0.5 and 9 sqrt(3)/2, and therefore a hypotenuse:

BC = BC' = sqrt { (1/2^2 + [9 sqrt(3)/2 ]^2 } = 7.81 cm

The number, miscopied was AC = AD -0.5 = AB cos 60 -.05

= 9 x 1/2 - 0.5 = 4 cm. He wrote 5 cm.

Edited on August 30, 2018, 1:22 pm
  Posted by Steven Lord on 2018-08-30 09:14:57

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