Trigonometry & Inverse Trigonometry
Two Observers at Different Directions — Distance Between Them
nta_pyq_2023_apr
Grade 11
Question:
The angle of elevation of the top $P$ of a tower from the feet of one person standing due south of the tower is $45°$ and from the feet of another person standing due west of the tower is $30°$. If the height of the tower is 5 meters, then the distance (in meters) between the two persons is equal to
\dfrac{5\sqrt{5}}{2}
10
5
5\sqrt{5}
Step-by-Step Solution
Key Concept: South person: $\tan45°=\frac{5}{x_1}\Rightarrow x_1=5$. West person: $\tan30°=\frac{5}{x_2}\Rightarrow x_2=5\sqrt{3}$.
$AB=\sqrt{25+75}=10$ m.
Correct Answer: 2