KnowledgeBoat Logo
|

Mathematics

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

28 Likes

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.

Answered By

15 Likes

Related Questions