Math Problem Statement

Danielle is facing towards town A, which is at a bearing of 300° from her. If she turns 135° clockwise, she will be facing towards town B. What is the bearing of town B from Danielle?

Solution

Let's break down the problem to find the bearing of town B from Danielle:

  1. Initial Bearing of Town A: Danielle is facing town A at a bearing of 300°.

  2. 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°):

300+135=435300^\circ + 135^\circ = 435^\circ

Since bearings are typically given in the range of 0° to 360°, we need to subtract 360° to normalize the value:

435360=75435^\circ - 360^\circ = 75^\circ

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:

  1. What are bearings and how are they measured?
  2. What is the difference between clockwise and counterclockwise directions in bearings?
  3. How do you normalize an angle greater than 360°?
  4. Can bearings ever be negative? Why or why not?
  5. 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