RD Sharma Solutions Class 10 Mathematics Solutions for Some Applications Of Trigonometry Exercise 12.1 in Chapter 12 - Some Applications Of Trigonometry
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A kite is flying at a height of 75 meters from the ground level, attached to a string inclined at 60° to the horizontal.
Find the length of the string to the nearest meter.
Solution:
A common notion in trigonometry, specifically, is the angle of elevation, which has to do with height and distance. It is described as an angle formed by the horizontal plane and an oblique line between the observer's eye and a target above it.
Given,
Height of kite flying from the ground level = 75 m = AB
Angle of inclination of the string with the ground (θ) = 60°
Let the length of the string be L = AC
So, from the figure formed we have △ABC as a right triangle.
Hence,
\begin{aligned} &\sin \theta=\frac{\text { opposite side }}{\text { hypotenuse }} \\ &\sin 60^{\circ}=\frac{\mathrm{AB}}{\mathrm{AC}} \end{aligned}
\begin{aligned} &\frac{\sqrt{3}}{2}=\frac{75}{L} \\ &L=50 \sqrt{3} \mathrm{~m} \end{aligned}
\text { Length of string } \mathrm{L}=50 \sqrt{3} \mathrm{~m}
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