Question

3 A surveyor has to determine the distance

Answer 1

According to the solving the distance from A to B is = 374.16m.

Distance between two points:

Except when the points meet, distances in geometry have always been positive. The distance between A and B is the same as that between the distance between B and A. We consider two points A(a,b) and B to get the formula for such distance between two points in the plane (c,d).

What do you call the distance between two points?

A line segment's length is the distance between two points. Congruent segments are those with the same length. We can calculate the distance between these two points by drawing a line with a ruler.

According to the given data:

Given:

BÂC = 45°

ACB = 55°

We know that sum of all angles:

ABC + BAC + ACB = 180

ABC =  180 -  BAC + ACB

        = 180 - 45 -55

        = 80.

AC = 450

$\frac{AC}{sin ABC} = \frac{AB}{sin ACB}$

AB = $\frac{AC . sin ACB}{sin ABC}$

= $\frac{450 * sin55}{sin80}$

= 374.16m

The distance from A to B is 374.16m.

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