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?
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 |
solution
