From a point o in a school compound adeolu is 100m away on a bearing of N35 degree east and ibrahim isv80 m away on a bearing of S55 degree west
A) how far are both boys
B) what is the bearing of Ibrahim from adeolu in 3 figure bearing
A) To find the distance between both boys, we can use the cosine rule:
d^2 = 100^2 + 80^2 - 2(100)(80)cos(145)
d^2 = 10000 + 6400 + 16000cos(145)
d^2 = 26400 + 16000(-0.5736)
d^2 = 16192
d ≈ 127.2 meters
Therefore, both boys are approximately 127.2 meters apart.
B) To find the bearing of Ibrahim from Adeolu, we can use the inverse tangent function:
tanθ = (opposite/adjacent)
tanθ = (80 sin55)/(100 cos35)
tanθ ≈ 0.7321
θ ≈ 36.87 degrees
However, we need to determine whether Ibrahim is to the east or west of Adeolu. Since Ibrahim is on a bearing of S55 degrees west, we subtract his direction from 180 degrees (which is due north) to get his true bearing:
180 - 55 = 125 degrees
Therefore, Ibrahim is approximately N36°W from Adeolu, or in 3-figure bearing: 036°.
A) To find the distance between Adeolu and Ibrahim, we can use the cosine rule.
Distance² = a² + b² - 2ab * cos(C)
Where:
a = 100m (distance to Adeolu)
b = 80m (distance to Ibrahim)
C = angle between the two distances
To find C, we can use the fact that the sum of angles in a triangle is 180 degrees.
C = 180 - (35 + 55) = 90 degrees
Now let's plug in the values into the formula:
Distance² = 100² + 80² - 2 * 100 * 80 * cos(90)
Distance² = 10000 + 6400 - 2 * 100 * 80 * 0
Distance² = 16400
Distance = √16400
Distance ≈ 128.06m
So, the distance between Adeolu and Ibrahim is approximately 128.06 meters.
B) To find the bearing of Ibrahim from Adeolu, we can use trigonometry.
Since Adeolu is facing N35 degrees east, the angle between the north direction and the direction to Ibrahim is 35 + 90 = 125 degrees.
To find the bearing, we subtract this angle from 360 degrees:
Bearing = 360 - 125
Bearing = 235 degrees
Therefore, the bearing of Ibrahim from Adeolu is 235 degrees (in 3 figure bearing).