A road that at a college and goes due north for 2,000 m it then goes 2,000 m on a bearing 040° and end as a market .
a .how far is the market from the college ?
b.what is the bearing of the market from the College?
a. To find the distance between the college and the market, we can use the Pythagorean theorem:
Distance = √(2000^2 + 2000^2)
Distance = √(4,000,000 + 4,000,000)
Distance = √8,000,000
Distance ≈ 2,828.43 meters
Therefore, the market is approximately 2,828.43 meters from the college.
b. To find the bearing of the market from the college, we can use trigonometry.
First, we can find the angle that the road makes from due north:
tanθ = opposite / adjacent
tanθ = 2000 / 2000
θ = tan^(-1)(1)
θ ≈ 45°
Next, we can add the given bearing (040°) to the angle of the road:
Bearing = 45° + 40°
Bearing = 85°
Therefore, the market is 85° from due north.