In surveying, sometimes a value can be found for an inaccessible length l (such as the height of a tall free) by measuring other three length l 1 , l 2 , l 3 in terms of which l l 3 l 1 l 2

Question

In surveying, sometimes a value can be found for an inaccessible length $l$ (such as the height of a tall free) by measuring other three length $l_{1}, l_{2}, l_{3}$ in terms of which $l \frac{l _{1} l _{2}}{l _{3}}$ . Suppose we perform such an experiment and obtain the following results (in feet) $l_{1} = 200 \pm 2, l_{2} = 5.5 \pm 0.1, l_{3} = 10.0 \pm 0.4$ . If in this experiment value of ' $l$ ' is expressed as $l = 110 \pm x$ , find value of ' $x$ ' (in feet)

Answer:

8

Solution:

$l_{best} \frac{200 \times 5.5}{10.0} = 110$ . Now $\frac{δ 1}{l} = \frac{δ l _{1}}{l _{1}} + \frac{δ l _{2}}{l _{2}} + \frac{δ l _{3}}{l _{3}} = 7.5%$ So final answer is $l = (110 \pm 8) ft$

TestHub · Accepted Answer

l best ​ 10.0 200 × 5.5 ​ = 110 . Now l δ 1 ​ = l 1 ​ δ l 1 ​ ​ + l 2 ​ δ l 2 ​ ​ + l 3 ​ δ l 3 ​ ​ = 7.5% So final answer is l = ( 110 ± 8 ) ft

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