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

Question

A) how far are both boys
B) what is the bearing of Ibrahim from adeolu in 3 figure bearing

Answer 1

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°.