Question 159

A kite is flying at the height of 75m from the ground. The string makes an angle θ (where cotθ = 8/15) with the level ground. Assuming that there is no slack in the string the length of the string is equal to :

Solution

Height of kite from ground = AB = 75 m

$$\angle$$ACB = $$\theta$$

We know that $$cot\theta = \frac{8}{15}$$

=> $$\frac{BC}{AB} = \frac{8}{15}$$

=> $$BC = \frac{8*75}{15} = 40 m$$

Now, length of string AC = $$\sqrt{(AB)^2 + (BC)^2}$$

=> AC = $$\sqrt{75^2 + 40^2}$$

= $$\sqrt{5625+1600} = \sqrt{7225}$$

=> AC = 85 m

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