The construction of a triangle ABC in which A | vedclass

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Question

(B) In the construction of a triangle $ABC$ where the base $AB$ and the base angle $\angle A$ are given,the construction of the triangle is possible i

Vedclass · Accepted Answer

$4.5$

Vedclass · Answer

(B) In the construction of a triangle $ABC$ where the base $AB$ and the base angle $\angle A$ are given,the construction of the triangle is possible if the difference between the other two sides ($BC - AC$ or $AC - BC$) is less than the length of the base $AB$.According to the triangle inequality theorem,the difference of any two sides of a triangle must be less than the third side.Here,the base $AB = 4 \, cm$.Therefore,for the triangle to be constructible,the difference $|BC - AC|$ must be strictly less than $AB$.$|BC - AC| Checking the options:$(A)$ $3.5 $(B)$ $4.5 > 4$ (Not possible)$(C)$ $3 $(D)$ $2.5 Thus,the construction is not possible when the difference is $4.5 \, cm$.

The construction of a triangle $ABC$ in which $AB = 4 \, cm$ and $\angle A = 60^{\circ}$ is not possible when the difference of $BC$ and $AC$ is equal to: (in $cm$)

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