A kite is flying at a height of 75 m. If the string makes an angle \(\theta\) with the horizontal plane such that \(\tan\theta=\displaystyle\frac{15}{8}\), then find the length of the string.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 85 m
The height of the kite, the ground below the string and the string make a right triangle; the string is its hypotenuse. \(\tan\theta=\frac{15}{8}\) means height : ground distance = 15 : 8, and the hypotenuse of a 15 : 8 triangle is 17 (\(15^2+8^2=289=17^2\)), so \(\sin\theta=\frac{15}{17}\).
\(\sin\theta=\displaystyle\frac{\text{height}}{\text{string}}\), so string \(=\displaystyle\frac{75}{15/17}=75\times\frac{17}{15}=85\,\mathrm{m}\)
