 Hello and welcome to the session. In this session we discuss the final question which says, find the value of sin 30 degrees geometrically. Before we proceed with the solution, let's recall the RHS congruency rule. According to this we have if in two triangles, hypotenuse one side of a triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent. This is the key idea to be used in this question. Let's move on to the solution now. We need to find the value for sin 30 degrees geometrically for this. First of all we take the triangle ABC be an equilateral triangle. So this is triangle ABC which is an equilateral triangle. We take let the sides AB, BC and CA be equal to 2A. Now since triangle ABC is equilateral triangle, therefore angle A is equal to angle B is equal to angle C is equal to 60 degrees. Now next we draw AD perpendicular to BC. So we have this AD is perpendicular to BC. Next we consider the triangles ABD and ACD. Here we have AB is equal to AC which is equal to 2A since it is an equilateral triangle. Then we have AD is equal to AD which is the common side. Then angle BDA is equal to angle CDA each is equal to 90 degrees since we have AD perpendicular to BC. So therefore we have triangle ABD is congruent to the triangle ACD using the RHS congruence rule stated in the key idea. Now since these two triangles are congruent, this means that BD is equal to CD since these are the corresponding parts of the congruent triangle that is CPCT and each would be equal to 2A upon 2 since BC is equal to 2A. So we get BD is equal to CD is equal to A. Also angle BAD would be equal to angle DAC and each would be equal to the measure of angle A upon 2 which is equal to 60 degrees upon 2 and thus this is equal to 30 degrees since they are the corresponding parts of the congruent triangle so they are equal. Thus we have angle BAD is equal to angle DAC and each is equal to 30 degrees. Now consider the right triangle ABD in this we have sine 30 degrees is equal to perpendicular that is BD upon the hypotenuse which is AB. Now we got BD equal to A. So this is A upon 2A this AA cancels and this is equal to 1 upon 2 thus we get sine 30 degrees is equal to 1 upon 2 thus we get the value for sine 30 degrees as 1 upon 2 geometrically. So this completes the session hope you have understood the solution of this question.