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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