Question

construction of a triangle ABC in which AB equal to 4 cm angle a is equal to 60 degree is not possible when the difference of bc and ac equal to​

Answer 1

Answer:

Step-by-step explanation:

In ΔABC, ∠BAC=60° and AB=4 cm. (Given)..... (1)

First of all, we assume that BC=AC ..... (2)

Now we will calculate the lengths of BC or AC to satisfy condition (1).

From the diagram, it is clear that, if CD⊥AB, then D must be the mid point of AB. {As, BC=AC}

Then, AD= DB =2 cm ..... (3)

So, from the right angled ΔADC,

Cos∠CAD= AD/AC

⇒Cos 60°= 2/AC {From (1) and (3)}

⇒1/2= 2/AC

⇒AC=4 cm.

⇒BC=4 cm. {From equation (2)}

Therefore, BC or AC can not be equal