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Proof for Validation for Construction of a Triangle with Given Base, Base Angle and Difference between Two Sides

The construct...

Question

The construction of a $∆ A B C$ in which $A B = 7 c m, ∠ A = 75 °$ is possible when $(B C - A C)$ is equal to

$7.5 c m$

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$7 c m$

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$8 c m$

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$6.5 c m$

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Solution

The correct option is D
$6.5 c m$

Explanation for the correct option: (d)
Step 1: Given data:
In $∆ A B C$ ,
We have
$A B = 7 c m a n d ∠ A = 75 °$
Step 2: Rules for constructing a triangle:
Since we know that the sum of two sides of a triangle is greater than the third side.
So,
$A B + A C > B C \Rightarrow 7 + A C > B C \Rightarrow 7 > B C - A C$
Therefore,(d) is the correct option. Because $7 c m > 6.5 c m$

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The construction of a $∆ A B C$ , given that $B C = 3 c m, ∠ C = 60 °$ is possible when difference of $A B a n d A C$ is equal to:

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