Math Problem Statement
Solution
We are tasked with calculating the bearing of point from point .
Step-by-step approach:
-
Identify the right triangle: The diagram shows a right-angled triangle with:
- (the horizontal distance)
- (the vertical distance).
-
Bearing definition: A bearing is measured clockwise from north. We need to find the angle , where is the angle between line and the north direction from .
-
Trigonometric relationship:
- The bearing angle can be found using the tangent function, since we have the opposite side and the adjacent side :
-
Calculate the angle:
Let me calculate this for you.The bearing of point from point is , measured clockwise from north.
Would you like more details or have any questions?
Here are some related questions to expand on this concept:
- How do bearings change when distances are reversed between points?
- How can you use other trigonometric functions to find angles in similar problems?
- What is the significance of the right triangle in navigation problems like this one?
- How would the bearing change if point was directly east of point ?
- How can Pythagoras' Theorem be used to check the distances in this problem?
Tip: Bearings are always measured clockwise from the north, and a full bearing can range from to .
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Bearings
Right-Angled Triangle
Formulas
tan(θ) = opposite / adjacent
θ = tan⁻¹(opposite/adjacent)
Theorems
Pythagorean Theorem
Trigonometric Ratios
Suitable Grade Level
Grades 10-12
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