Case Study – 2 Radio towers are used for transmitting a range of communication services including radio and…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 4 Marks · March 2024 · Standard
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274 Marks · March 2024 · Standard
Case Study – 2 Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two stations A and B (B vertically below A). The tower is supported by wires AO and BO from a point O on the ground. Distance between the base C of the tower and the point O is $36$ m. From O, the angles of elevation of the tops of station B and station A are $30^\circ$ and $45^\circ$ respectively. Based on the above, answer the following questions : (i) Find the height of station B. (ii) Find the height of station A. (iii) (a) Find the length of the wire OA. OR (b) Find the length of the wire OB.
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(i) $$\begin{aligned}& \tan 30^\circ = \frac{BC}{36} = \frac{1}{\sqrt{3}} \\ & \Rightarrow BC = 12 \sqrt{3}\end{aligned}$$ m (ii) $$\begin{aligned}& \tan 45^\circ = \frac{AC}{36} = 1 \\ & \Rightarrow AC = 36\end{aligned}$$ m (iii) (a) $$\begin{aligned}& \sec 45^\circ = \frac{OA}{36} = \sqrt{2} \\ & \Rightarrow OA = 36\sqrt{2}\end{aligned}$$ m OR (iii) (b) $$\begin{aligned}& \sec 30^\circ = \frac{OB}{36} = \frac{2}{\sqrt{3}} \\ & \Rightarrow OB = 24\sqrt{3}\end{aligned}$$ m
