Let ABC be a triangle with area 36 square cm. If AB = 9 cm, BC = 12 cm and \angle ABC=\theta, then what is \cos \theta equal to?

  1. A. \frac{\sqrt{5}}{3} ✓
  2. B. \frac{\sqrt{5}}{4}
  3. C. \frac{1}{3}
  4. D. \frac{2}{3}

Correct Answer: A. \frac{\sqrt{5}}{3}

Explanation

Area of \triangle ABC = \frac{1}{2} \times AB \times BC \times \sin \theta. Substituting values: 36 = \frac{1}{2} \times 9 \times 12 \times \sin \theta \implies \sin \theta = \frac{2}{3}. Then \cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - \frac{4}{9}} = \frac{\sqrt{5}}{3}.

Related questions on Geometry

Practice more CDS Elementary Mathematics questions