Bearings and direction word problems

Bearings and direction word problems

Lessons

Theorems that are useful:

Pythagorean Theorem: a2+b2=c2a^{2} + b^{2} = c^{2}

Trig ratio: sinθ=OH\sin \theta = \frac{O}{H}

cosθ=AH\cos \theta = \frac{A}{H}

tanθ=OA\tan \theta = \frac{O}{A}

Law of sine: asinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Law of cosine: c2=a2+b22abcosCc^{2} = a^{2} + b^{2} - 2ab \cos C

  • Introduction
    Introduction to Bearings and Direction Word Problems

  • 1.
    Evaluate A Bearings Word Problem Using Trigonometric Ratios

    Charlie leaves home for a bike ride, heading 040°T for 5km.

    a)
    How far north or south is Charlie from its starting point?

    b)
    How far east or west is Charlie from its starting point?


  • 2.
    Solve A Bearings Word Problem Using the Law of Cosine

    A camping group made a return journey from their base camp. From the camp, they first travelled 120°T for 3km. Then they travelled 210°T for 9km. Determine the direction and distance they need to travel if they want to return to the base camp now.


  • 3.
    Analyze A Bearings Word Problem Using Trigonometric Ratios and the Law of Cosine

    Melody and April go to the same school. Melody's home is 3.5km with a bearing of S16°W from school whilst April's home is 2.4km with a bearing of N42°E from school. How far away are their homes from each other?


  • 4.
    Triangulate the Location of an Earthquake

    Radar X detected an earthquake N55°E of it. 16km due east of Radar X, Radar Y detected the same earthquake N14°W of it.

    a)
    Determine the earthquake from Radar X and Y.

    b)
    Which Radar is closer to the earthquake?


  • 5.
    Estimate the Height of an Object

    A plane is sighted by Tom and Mary at bearings 028°T and 012°T respectively. If they are 2km away from each other, how high is the plane?


  • 6.
    Applying Law of Sine and Law of Cosine

    Consider the following diagram.

    Applying Law of Sine and Law of Cosine

    Find the distance between P and Q.