The length of line AE for the following traverse will be

Line Length (m) Bearing

$A B$ $400$ $30^{o}$

$B C$ $500$ $0^{o}$

$C D$ $600$ $300^{o}$

$D E$ $400$ $30^{o}$

1300 m

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1500 m

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1600 m

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1400 m

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Solution

The correct option is B $1500 m$
Assuming A as origin

Consecutive points Coordinates:

Point B $L = 400 c o s 30^{o} = 346.41 m$
$D = 400 s i n 30^{o} = 200 m$

Pint C $L = 500 c o s 0^{o} = 500 m$
$D = 500 s i n 0^{o} = 500 m$

Point D $L = 600 c o s 60^{o} = 300 m$
$D = - 600 s i n 60^{o} = - 519.6 m$

Point E $L = 400 c o s 30^{o} = 346.4 m$
$D = 400 s i n 30^{o} = 200 m$

Independent Coordinates

$A$ $(0, 0)$

$B$ $(346.4, 200)$

$C$ $(346.4 + 500 = 846.4, 200 + 0 = 200)$

$D$ $(846.4 + 300 = 1146.4, 200 - 519.6 = - 319.6)$

$E$ $(1146.4 + 346.4 = 1492.8, - 319.6 + 200 = - 119.6)$

Hence, Length $A E = \sqrt{(0 - 1492.8)^{2} + (0 - (- 119.6))^{2}}$
$= 1498 m ≃ 1500 m$ (say)

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