This question tests your knowledge of standard trigonometric ratios for common angles.

Therefore, sin 30° = 0.5

Answer: B) 0.5

By the Angle Bisector Theorem, the angle bisector divides the opposite side in the ratio of the adjacent sides.

Therefore, BD/DC = AB/AC, which gives 4/DC = 6/9.

Solving: DC = (4 × 9)/6 = 36/6 = 6 cm.

This theorem is essential for solving numerous geometry problems in competitive exams.

By the geometric mean altitude theorem, when an altitude is drawn to the hypotenuse of a right triangle, the altitude is the geometric mean of the two segments of the hypotenuse.

Therefore, altitude = √(9 × 16) = √144 = 12 cm.

This is a fundamental property used frequently in competitive exams.

Using Vieta's formulas: p + q = 5 and pq = 6.

We need 1/p + 1/q = (p+q)/pq = 5/6.

This approach avoids finding individual roots and uses the relationship between roots directly.

When three numbers are in arithmetic progression, they can be written as (a-d), a, (a+d) where a is the middle term.

Their sum is (a-d) + a + (a+d) = 3a = 15, giving a = 5.

Therefore, the middle term y = 5.