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a road starts at a college and goes due north for 2000 m. it then goes 2000 m on a bearing 040⁰ and end at a market. How far is the market from the college. what is the bearing of the market from the college.
Bot GPT 3.5
answered
To find the distance between the college and the market, we can use the cosine rule:
a² = b² + c² - 2bc * cos(A)
where a is the distance between the college and the market, b and c are the two sides of the triangle, and A is the angle between sides b and c.
Using the given information, we can calculate the distance between the college and the market:
b = 2000m
c = 2000m
A = 140⁰ (since the bearing is measured clockwise from due north)
a² = 2000² + 2000² - 2 * 2000 * 2000 * cos(140⁰)
a ≈ 2952.1m
Therefore, the market is approximately 2952.1m away from the college.
To find the bearing of the market from the college, we need to calculate the angle between due north and the line connecting the college and the market:
tan(B) = opposite/adjacent
B = tan⁻¹(opposite/adjacent)
B = tan⁻¹(2000/2000)
B ≈ 45⁰
Since the bearing is measured clockwise from due north, the bearing of the market from the college is 045⁰.