Trigonometry & Inverse Trigonometry
Heights And Distances
nta_abhyas_2025
Grade 11
Question:
A tower subtends angles $\alpha$, $2\alpha$ and $3\alpha$, respectively, at points $A$, $B$ and $C$ all lying on a horizontal line through the foot of the tower. If $\frac{AB}{BC} = 1 + p \cos p\alpha$, then the value of $p$ is
Step-by-Step Solution
Key Concept: Angles in a height and distance problem involving multiple observation points can be decomposed into components
From the given information, $\angle APB = \angle PBC - \angle BAP = 2\alpha - \alpha = \alpha$. Similarly, $\angle BPC = \alpha$ and $\angle CPM = \alpha$. These equal angles indicate that the angles subtended at successive points along the configuration are all equal to $\alpha$.
Correct Answer: 25