Exercise - 3.10

. Determine whether the following measurements produce one triangle, two triangles or no triangle: ∠ B = ◦ , a = , b = . Solve if solution exists. .

If the sides of a △ ABC are a = , b = and c = , then show that cos B + cos C = . . In a △ ABC , if a = − , b = + and C = ◦ , find the other side and other two angles. .

In any △ ABC , prove that the area △ = b + c − a cot A . . In a △ ABC , if a = cm , b = cm and C = ◦ , then show that its area is sq.cm. .

In a △ ABC , if a = cm , b = cm and c = cm , then show that its area is sq.cm. . Two soldiers A and B in two different underground bunkers on a straight road, spot an intruder at the top of a hill. The angle of elevation of the intruder from A and B to the ground level in the eastern direction are ◦ and ◦ respectively.

If A and B stand km apart, find the distance of the intruder from B . . A researcher wants to determine the width of a pond from east to west, which cannot be done by actual measurement. From a point P , he finds the distance to the eastern-most point of the pond to