Possible or not

Geometry Level 2

Can a triangle with following measurements possible?

Triangle ABC with Angle B = 60°, BC = 3, AC = 2.

Yes No

Vaibhav Priyadarshi by Vaibhav Priyadarshi , 17, India

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1 solution

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Jul 2, 2018

If A B ‾ = x \overline{AB}=x ,then A C ‾ 2 = B C ‾ 2 + A B ‾ 2 − 2 B C ‾ × A B ‾ × cos ⁡ B = 9 + x 2 − 3 x = ( x − 1.5 ) 2 + 6.75 ≥ 6.75 \overline{AC}^2=\overline{BC}^2+\overline{AB}^2-2\overline{BC}\times\overline{AB}\times\cos B=9+x^2-3x=(x-1.5)^2+6.75\ge6.75

A C ‾ ≥ 6.75 ≈ 2.6 \overline{AC}\ge\sqrt{6.75}\approx2.6 ,but A C ‾ = 2 \overline{AC}=2 ,which is not bigger than 2.6 2.6

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