Let `A B Ca n dA B C '` be two non-congruent triangles with sides `A B=4,A C=A C^(prime)=2sqrt(2)` and angle `B=30^0` . The absolute value of the difference between the areas of these triangles is

If A, B, C are the angles of a triangle then tan ((B+C)/2)=

In triangle ABC, sinA sin B + sin B sin C + sin C sin A = 9//4 and a = 2 , then the value of sqrt3 Delta , where Delta is the area of triangle, is _______

A, B and C are interior angles of a triangle ABC, then sin ((B + C)/(2)) =

If the angles of a triangle are 30^0a n d45^0 and the included side is (sqrt(3)+1)c m then the area of the triangle is______.

Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b : c be sqrt(3):sqrt(2) . Find angle Adot

In a triangle ABC, if (cos A)/(a) =(cos B)/(b ) =(cos C)/(c) and the side a=2, then the area of the triangle is-

Let the area of triangle ABC be (sqrt3 -1)//2, b = 2 and c = (sqrt3 -1), and angleA be acute. The measure of the angle A is

When any two sides and one of the opposite acute are given, under certain additional condition two triangle are possible. The case when two triangle are possible is called the ambiguous case. In fact when any two sides and the angle opposite to one of them are given either no triangle is possible or only one triangle is possible or two triangle are possible. In the ambiguous case, let a, b, and angleA are given and c_1,c_2 are two values of the third side c The difference between two values of c is

Given b=2,c= sqrt3 and A= 30^@, then in-radius of triangle ABC is

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is