Question : The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is $\frac{5}{9}$ metres, then what is the distance (in metres) between the two poles?
Option 1: 63
Option 2: 30
Option 3: 25
Option 4: 45
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Correct Answer: 45
Solution : In the figure, two poles AB and PQ of height 60 m & 35 m are connected by rope BQ. Rope BQ is making angle θ with the horizontal whose tangent is $\frac{5}{9}$metre; $\therefore$ BO = 60 – 35 = 25 metres Now, tan θ =$\frac{BO}{OQ}$ ⇒ $\frac{5}{9} = \frac{25}{OQ}$ $\therefore$ OQ = 45 metres Hence, the correct answer is 45.
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