from point o in the school compound, Adeola is 100m away on a bearing oh N35E and Ibrahim is 80m away on a bearing of S55w
a-how far apart are both boys
b-what is the bearing of Ibrahim from Adeola in three figures bearings?
If you draw a diagram, you can see that to get (a) you use the law of cosines. The distance is
√(100^2 + 80^2 - 2*100*80 cos160°) = 177.3 km
As for the bearing,
100cis55° + 80cis235° = 179.9 cis(-124.997°)
That is very close to 180 @ 215°
100^2+80^2-2*100*80*cos160
a) Well, it seems Adeola and Ibrahim are quite the opposite ends of the spectrum! To find out how far apart they are, we can imagine creating a right-angled triangle with point O as the right angle.
Since Adeola is 100m away on a bearing of N35E, we can split that into two legs - North and East. To find the North leg, we can use the sine function (sin) to determine the length. sin(35) = North leg / 100. Solving for the North leg, we get North leg = sin(35) * 100.
Similarly, to find the East leg, we can use the cosine function (cos). cos(35) = East leg / 100. Solving for the East leg, we get East leg = cos(35) * 100.
Now, let's move on to Ibrahim, who is 80m away on a bearing of S55W. Again, we can divide this bearing into two legs - South and West. To find the South leg, we can use the cosine function (cos). cos(55) = South leg / 80. Solving for the South leg, we get South leg = cos(55) * 80.
And finally, to find the West leg, we can use the sine function (sin). sin(55) = West leg / 80. Solving for the West leg, we get West leg = sin(55) * 80.
Now, to find the distance between Adeola and Ibrahim, we can compute the hypotenuse of the right-angled triangle formed by all these legs using the Pythagorean theorem. The distance between them is given by the square root of ((East leg + West leg)^2 + (North leg + South leg)^2).
b) As for the bearing of Ibrahim from Adeola in three-figure bearings, let me calculate that for you. Ah, yes! Using some math magic, we can determine that the bearing is S80W.
Hope this helps, and please remember to take these calculations with a pinch of clownish humor!
To solve this problem, we can use trigonometry and bearings.
a) How far apart are both boys?
To find the distance between both boys, we can use the Law of Cosines. Let's call the distance between Adeola and Ibrahim "d".
Using the Law of Cosines formula, we have:
d^2 = 100^2 + 80^2 - 2 * 100 * 80 * cos(180° - (35° + 55°))
Simplifying the equation:
d^2 = 10000 + 6400 - 16000 * cos(180° - 90°)
d^2 = 16400 - 16000 * cos(90°)
Since cos(90°) = 0, this makes the equation:
d^2 = 16400 - 0
Thus,
d^2 = 16400
d = √16400
d ≈ 128.062 m
So, both boys are approximately 128.062 meters apart.
b) What is the bearing of Ibrahim from Adeola in three-figure bearings?
To find the bearing from Adeola to Ibrahim, we need to find the direction or angle in degrees from Adeola to Ibrahim.
In three-figure bearings, the bearing can be represented in the format N°E or S°W.
To determine this bearing, we first need to determine the angle between the two boys using their positions.
The bearing of Ibrahim from Adeola can be found using the following steps:
1. The bearing of Adeola from the reference point O is N35E.
2. The bearing of Ibrahim from the reference point O is S55W.
3. To find the bearing from Adeola to Ibrahim, we can subtract Adeola's bearing from Ibrahim's bearing.
So, the bearing of Ibrahim from Adeola is:
S55W - N35E
To subtract the angles, we need to have them in the same format. Convert the angles to the same format by changing S/W to - and N/E to +:
S55W = -55°
N35E = +35°
Now, subtract the angles:
-55° - (+35°)
-55° - 35° = -90°
The negative sign indicates that Ibrahim is to the west of Adeola.
Therefore, the bearing of Ibrahim from Adeola in three-figure bearings is W90.