The difference between the two acute angleof a right angled triangle is (2pi)/(5) radians. Express the angles in degrees.

If one of the sides and any other part (either an acute angle or any side) of a right angle triangle is known, the remaining sides and angles of the triangle can be determined. Do you agree? Explain with an example.

The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the given figure. The students are to sow seeds of flowering plans on the remaining area of the plot. (1) Taking A as origin, find the coordinates of the vertices of the triangle. (2) What will be the coordinates of the vertices of Delta PQR if C is the origin ? Also calculate the areas of the triangles in these cases. What do you observe ?

Show that the relation R defined in the set A of all polygons as R = {(P_(1),P_2):P_1 and P_2 have same number of sides} , is an equivalence relation . What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ?

Show that the relation R defined in the set A of all triangles as R={(T _(1), T _(2))):T _(1) is similar to T _(2) } is equivalence relation. Consider three right angle triangles T_(1) with sides 3,4,5,T_(2) with sides 5,12,13 and T_(3) with sides 6,8,10. Which triangles among T_(1), T_(2) and T_(3) are related ?

Show that the relation R defined in the set A of all triangles as R = {(T_(1),T_(2)}T_(1) is similar to T_2 } , is equivalence relation . Consider three right angle triangles T_1 with sides 3,4,5 , T_2 with sides 5,12, 13 and T_3 with sides 6, 8, 10 . Which triangles among T_1 , T_2 and T_3 are related ?

Cut a right angled triangle, stick a string along its perpendicular side, as shown in fig. (i) hold the both the sides of a string with your hands and rotate it with constant speed. What fo you observe?

If the sum of the lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum when the angle between them is (pi)/(3) .

What happen if the angle in the circle segment is right angle? What kind of segment do you obtain? Draw the figure and give reason.

Three concurrent force of the same magnitude are in equilibrium. What is the angle between the forces? Also name the triangle formed by the forces as sides.