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IB Maths AI SL 3.2 Triangle trigonometry

IB Maths AI SL 3.2 Triangle trigonometry
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise solving non-right and right triangle problems using sine rule, cosine rule, area formula, and bearing calculations from diagrams and field data.

How this is tested

  • use cosine rule to find angle BÂC when three side lengths of triangle ABC are known or derivable
  • apply cosine rule to find DC given two sides and included angle of 170° in triangle DBC
  • calculate NV or PN̂V in a triangle with two sides and included angle using cosine or sine rule

Question 6(a)

[Maximum number: 3]

Triangle ABC has sides of length AB=10 cm,BC=8 cm\mathrm{AB}=10 \mathrm{~cm}, \mathrm{BC}=8 \mathrm{~cm} and AC=15 cm\mathrm{AC}=15 \mathrm{~cm}, as shown in the diagram.

Find the size of BÂC.

The circular arc BD , with centre A , is drawn inside the triangle, such that D lies on AC .