bearing of a tower are taken from two points A and B 250m apart, along a straight line north-south path, A being due north of B.the bearing of the tower from A to B are 140* and 110* respectively.choose two option that gives a distance from A and B of the tower to nearest meter.
a)231 b)321 c)355 d)405 e)453 f)470 g)504 h)554
To find the distance from points A and B to the tower, we can use the concept of trigonometry and the given information about the bearings.
First, let's visualize the situation:
```
A --------> Tower
|
|
|
B
```
We know that A and B are 250 meters apart along a straight line, with A being due north of B. The bearings from A to the tower are 140° and 110° respectively.
To find the distance from point A to the tower, we can use the cosine rule:
cos(A) = adjacent side / hypotenuse
In this case, the adjacent side is the distance from point A to the tower, and the hypotenuse is the distance from point A to point B (250 meters).
For the bearing of 140°:
cos(140°) = adjacent side / 250
adjacent side = 250 * cos(140°)
Calculating this value:
adjacent side = 250 * cos(140°) ≈ 231.14
Therefore, the distance from A to the tower is approximately 231 meters.
Similarly, we can find the distance from point B to the tower using the bearing of 110°:
cos(110°) = adjacent side / 250
adjacent side = 250 * cos(110°)
Calculating this value:
adjacent side = 250 * cos(110°) ≈ 470.25
Therefore, the distance from B to the tower is approximately 470 meters.
From the given options, the two distances nearest to the ones we calculated are:
a) 231
f) 470
So the correct options are a) 231 and f) 470.