Math Problem Statement
Solution
The diagram you provided shows three tents , , and arranged in a right-angled triangle. We are tasked with calculating the bearing of point from point .
The information given is:
- Tent is 5 m due south of (vertical leg of the triangle).
- Tent is 7.5 m due west of (horizontal leg of the triangle).
Since the right angle is at , we need to find the bearing of from . Bearings are measured clockwise from the north direction. In this case, we need to find the angle that tent makes with respect to the north direction from .
Steps to Solve:
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Determine the angle using trigonometry: The triangle formed by , , and is a right triangle. The angle is the angle between the line and the vertical leg . We can use the tangent function: So,
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Calculate the value of :
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Calculate the bearing: Bearings are measured clockwise from the north, so we need to add to the calculated angle , because the direction of from is in the southwest quadrant. Thus, the bearing of from is:
Final Answer:
The bearing of from is approximately .
Would you like further details or explanations?
Here are 5 related questions to explore:
- How do you calculate a bearing if you are given coordinates instead of distances?
- What other trigonometric functions could be useful in finding angles in triangles?
- How would you calculate the distance between and ?
- What is the difference between true bearing and relative bearing?
- Can bearings ever be negative, and if so, how are they handled?
Tip: Always ensure you know whether bearings are being measured clockwise or counterclockwise, as this can impact the final answer significantly.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Bearings
Right-Angle Triangles
Formulas
tan(θ) = opposite / adjacent
θ = tan^(-1)(opposite / adjacent)
Bearing = 180° + θ
Theorems
Trigonometric Ratio (Tangent)
Suitable Grade Level
Grades 8-10
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