Directions: Each question is followed by two statements. Mark [1], if the question can be answered by using only one of the statements alone but not by using the other statement alone Mark [2], if the question can be answered by using either of the statements alone. Mark [3], if the question can be answered by using both the statements together but not by using either of the statements alone. Mark [4], if the question cannot be answered. What is the height of a tower installed on the top of a hill? I: Angle of elevation made by the bottom of the tower is 45 degrees and the top of the tower is 60 degrees from a point at a distance 'a' from the foot of the hill in the eastern direction. II: Angle of elevation made by the bottom of the tower is 30 degrees from a point at a distance 'a + 10' from the foot of the hill in the eastern direction.

Statement 1 provides two equations using the tangent of the elevation angles, where tan 45 equals the hill height divided by the distance a, and tan 60 equals the combined height of the hill and tower divided by a; because both the hill height and tower height are unknown variables, they cannot be solved independently from this statement alone. Statement 2 introduces a new equation with the hill height divided by the quantity a plus 10 equaling tan 30, but this also cannot yield the tower height independently. By substituting the value of the hill height from the first equation into the second equation to find a, you can then determine the hill height and subsequently calculate the tower height from the first statement. Therefore, the question can only be answered by using both statements together, making the result option 3.

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