Math Problem Statement
Solution
Let's break down the problem to find the bearing of town B from Danielle:
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Initial Bearing of Town A: Danielle is facing town A at a bearing of 300°.
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Clockwise Turn: She turns 135° clockwise to face town B.
To find the bearing of town B, we add the 135° turn to her initial bearing (300°):
Since bearings are typically given in the range of 0° to 360°, we need to subtract 360° to normalize the value:
So, the bearing of town B from Danielle is 75°.
Would you like further details or clarification on any step? Here are five related questions you might find helpful:
- What are bearings and how are they measured?
- What is the difference between clockwise and counterclockwise directions in bearings?
- How do you normalize an angle greater than 360°?
- Can bearings ever be negative? Why or why not?
- How would the problem change if Danielle turned counterclockwise instead?
Tip: When working with bearings, always remember they are measured clockwise from the north, and should be kept between 0° and 360°.
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Math Problem Analysis
Mathematical Concepts
Bearings
Clockwise Rotation
Angle Normalization
Formulas
New Bearing = Initial Bearing + Clockwise Rotation
Normalized Bearing = New Bearing - 360° (if New Bearing > 360°)
Theorems
Bearings are measured clockwise from the north and should be kept between 0° and 360°.
Suitable Grade Level
Grades 8-10
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