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 ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60° with the level of the ground.
Determine the height of the wall.
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,
Distance between the wall and the foot of the ladder = 2m = BC
Angle made by ladder with ground (θ) = 60°
Height of the wall (H) = AB
Now, the fig. of ABC forms a right angle triangle.
So,
\begin{aligned} &\tan \theta=\frac{\text { Opposite side }}{\text { Adjacent side }} \\ &\tan 60^{\circ}=\mathrm{AB} / \mathrm{BC} \\ &\sqrt{3}=\frac{\mathrm{AB}}{2} \\ &\mathrm{AB}=2 \sqrt{3} \\ &\therefore \text { Height of the wall }=2 \sqrt{3} \mathrm{~m} \end{aligned}
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