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From the figure, given below, calculate the length of CD.

From the figure, given below, calculate the length of CD. Heights and Distances, Concise Mathematics Solutions ICSE Class 10.

Heights & Distances

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Answer

From figure,

DE = CB = 15 m.

In ∆AED,

tan 22°=PerpendicularBase⇒0.404=AEDE⇒0.404=AE15⇒AE=15×0.404⇒AE=6.06 meters.\text{tan 22°} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow 0.404 = \dfrac{AE}{DE} \\[1em] \Rightarrow 0.404 = \dfrac{AE}{15} \\[1em] \Rightarrow AE = 15 \times 0.404 \\[1em] \Rightarrow AE = 6.06 \text{ meters}.

In ∆ABC,

tan 47°=PerpendicularBase⇒1.0724=ABBC⇒1.0724=AB15⇒AB=15×1.0724⇒AB=16.086 meters.\text{tan 47°} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow 1.0724 = \dfrac{AB}{BC} \\[1em] \Rightarrow 1.0724 = \dfrac{AB}{15} \\[1em] \Rightarrow AB = 15 \times 1.0724 \\[1em] \Rightarrow AB = 16.086 \text{ meters}.

From figure,

CD = BE = AB - AE

= 16.086 - 6.06

= 10.03 meters.

Hence, CD = 10.03 meters.

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