In a right-angled ABC , the measures of the angles are in an Arithmetic Progression (A.P.) If its smallest side is 4 units, then the area of ABC is.....

Step-by-step solution

Let the angles of the right-angled triangle be a - d , a , and a + d . The sum of the angles in a triangle is 180^ . (a - d) + a + (a + d) = 180^ 3a = 180^ a = 60^ Since the triangle is right-angled, the largest angle is 90^ . a + d = 90^ 60^ + d = 90^ d = 30^ The angles of the triangle are 30^ , 60^ , and 90^ . The smallest side is opposite to the smallest angle, which is 30^ . Let this side be x = 4 units. The other perpendicular side, opposite to 60^ , is y = x 60^ = 4 3 units. The area of the right-angled trian