Question 56

A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with the ground is 30°. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?

Solution

So, $$\tan30^{\circ\ }=\frac{PM}{PQ}=\frac{PM}{x}\ .$$

or, $$PM=\frac{x}{\sqrt{3}}\ .$$

So, $$x^2+\left(\frac{x}{\sqrt{3}}\right)^2=420^2\ .$$

or, $$x^2=420^2\times\frac{3}{4}\ .$$

or, $$x=363.7306\ .$$

So, $$PM=\frac{x}{\sqrt{3}}=\frac{363.7306}{\sqrt{3}}=210\ .$$

A is correct choice.

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