a road starts at a collage and goes due north for 2000m. it then 2000m on a bearing of 040 degrees and ends at a market. a.) how far is the market from the college? b.) what is the bearing of the market from the collage.
a) To find the distance from the college to the market, we can use the Pythagorean theorem because we have a right-angled triangle. The northward distance and the eastward distance form the two legs of the triangle, and the hypotenuse will give us the distance between the two points.
Using the Pythagorean theorem, the northward distance is 2000m, and the eastward distance can be calculated as follows:
Eastward distance = 2000m * cos(40°)
= 2000m * 0.766
Therefore, the eastward distance is approximately 1532m.
Now, we can calculate the distance between the college and the market:
Distance = √(2000^2 + 1532^2)
= √(4,000,000 + 2,349,824)
= √(6,349,824)
Thus, the market is approximately 2519.5 meters away from the college.
b) To find the bearing of the market from the college, we can use trigonometry. The bearing is measured clockwise from the north direction.
Using trigonometry, we can calculate the angle:
Angle = tan^(-1)(Eastward distance / Northward distance)
= tan^(-1)(1532 / 2000)
≈ tan^(-1)(0.766)
Using a calculator, the angle is approximately 36.87°.
Since the bearing is measured clockwise from the north, the bearing of the market from the college is approximately 360° - 36.87°.
Therefore, the bearing of the market from the college is approximately 323.13°.
To find the distance between the college and the market, we can use the Pythagorean theorem. The road goes due north for 2000m, and then another 2000m at a bearing of 040 degrees.
a) To find the distance, we can consider the two legs of a right-angled triangle. The first leg is the distance traveled north (2000m) and the second leg is the distance traveled at a bearing of 040 degrees (also 2000m). The hypotenuse of this triangle will be the distance between the college and the market.
Using the Pythagorean theorem, we can calculate the distance:
Distance = √((2000)^2 + (2000)^2)
Distance = √(4000000 + 4000000)
Distance = √(8000000)
Distance ≈ 2828.4m
Therefore, the market is approximately 2828.4 meters away from the college.
b) To find the bearing of the market from the college, we need to consider the angle between the direction due north and the road's bearing of 040 degrees. The bearing is usually measured clockwise from true north.
The angle between the direction due north and the road's bearing is 90 degrees (because the road goes straight north at the beginning) + 040 degrees (the additional bearing).
Therefore, the bearing of the market from the college is 90 + 40 = 130 degrees in a clockwise direction from true north.
Answer
Both Henry2 and I answered this same question yesterday using different approaches
Take your pick:
https://www.jiskha.com/questions/1827481/a-road-start-at-college-and-goes-due-north-for-2000m-it-then-2000m-on-a-bearing-of-040
btw, in that post "college" was spelled correctly.