Question

$\text{In each of the following cases,given reasons to show that the construction of}\Delta ABCisnotpossible:\left(i\right)AB=6cm,\angle A={40}^{\circ }and(BC+AC)=5.58cm\left(ii\right)AB=7cm,\angle A={50}^{\circ }and(BC-AC)=8cm\left(iii\right)BC=5cm,\angle B={80}^{\circ },\angle C={50}^{\circ },and\angle A={60}^{\circ }\left(iv\right)AB=4cm,BC=3cm,andAC=7cm.$

Answer 1

ANSWER:
(i) AB = 6 cm, $\angle A$ = 40° and ( BC + AC ) = 5.8 cm.
Here BC + AC is not greater than AB so, this triangle is not possible.
(ii) AB = 7 cm, $\angle A$ = 50° and ( BC – AC ) = 8 cm.
Here BC – AC is not less than AB so this triangle is not possible.
(iii) BC = 5 cm, $\angle B$ = 80°, $\angle C$ = 50° and $\angle A$ = 60°.
Sum of the angles of the given triangle is not equal to 180° so, given triangle is not possible.
(iv) AB = 4 cm, BC = 3 cm and AC = 7 cm.
Sum of two sides of this triangle not greater than the third side so given triangle not possible.