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Trigonometry

Question 4 of 9

Area of Triangle

Question

Given \(\triangle ABC\) with sides \(b = 4\,\text{cm}\), \(c = 6\,\text{cm}\) and an included angle \(A = 115^\circ\). Find the area of the triangle (Round your answer to 2 decimal places)

Show solution Hide solution Fully worked — 3 steps
Triangle ABC: vertex A at the bottom, vertex B above and to the left of A, and vertex C to the right of A. The angle at A, between sides c and b, is marked 115 degrees. Side c, from A up to B, is 6 cm; side b, from A to C along the base, is 4 cm; side a, from B to C, is unlabelled. The solution uses the two given sides b and c and their included angle A.
  1. State the formula
    \[ \mathit{area} = \frac{1}{2} bc \sin A \]
  2. Substitute values based on formula
    \[ \mathit{area} = \frac{1}{2}(4\,\text{cm})(6\,\text{cm})(\sin 115^\circ) \]
  3. Final answer

    Evaluate \(\frac{1}{2}(4\,\text{cm})(6\,\text{cm})(\sin 115^\circ)\):

    \[ \mathit{area} = 10.88\,\text{cm}^2 \]

    That is, the area of triangle ABC is 10.88 square centimetres, to 2 decimal places.