PrepRung
Sign inSign up free

NDA 2019 Maths · Mathematics · Properties of Triangles · easy

The area of a triangle with two sides 6 and 8 and the included angle 150^° is

Single correct option

The area of a triangle with two sides 66 and 88 and the included angle 150∘150^\circ is
  1. A. 1212
  2. B. 2424
  3. C. 12312\sqrt3
  4. D. 24324\sqrt3
Show answer and solution

Answer: (A) 1212

The area is 12absin⁡C=12⋅6⋅8⋅sin⁡150∘=24×12=12\dfrac12ab\sin C=\dfrac12\cdot6\cdot8\cdot\sin150^\circ=24\times\dfrac12=12. Since sin⁡150∘=sin⁡30∘=12\sin150^\circ=\sin30^\circ=\dfrac12, the obtuse angle does not change the formula. The value 2424 results from using sin⁡90∘\sin90^\circ or forgetting the factor 12\dfrac12, and the roots of 33 come from confusing with sin⁡60∘\sin60^\circ.
Report a mistake

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake