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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The angle of elevation of a ladder against a wall is 60° and the foot of the ladder is 9.5 m away from the wall.
Find the length of the ladder.
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 foot of the ladder = 9.5 m
Angle of elevation (θ) = 60°
Length of the ladder = L = AC
Now, from fig. ABC
ΔABC is a right angle triangle,
So,
\begin{aligned} &\cos \theta=\frac{\text { adjacent side }}{\text { hypotenuse }} \\ &\cos 60^{\circ}=\frac{\mathrm{BC}}{\mathrm{AC}} \\ &\frac{1}{2}=\frac{9.5}{\mathrm{AC}} \\ &\mathrm{AC}=2 \times 9.5=19 \mathrm{~m} \end{aligned}
**
Thus, length of the ladder (L) = 19 m**
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