Question

In a triangle ABC if a =13, b = 8 and c = 7, then find sin A.

• A. $\frac{1}{2}$
  
• B. $\frac{\sqrt{3}}{2}$
  
• C. $\frac{\sqrt{3}}{4}$
  
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}$


In trigonometry one problem can be solved in multiple ways but it is wise to use the best way to get the answer or at least not to use the lengthiest way. Here, we can apply sine rule and get the answer but have a look at the problem again. We are given all the sides. And when sides are given and angles are asked to find ,using cosine rule is a better option.
According to cosine rule -
$cosA=\frac{b^2+c^2-a^2}{2bc}$
$cosA=\frac{(8{)}^2+(7{)}^2-(13{)}^2}{2\left(8\right)\left(7\right)}$ (On putting values of a,b & c)
$cosA=-\frac{1}{2}$
$A=\frac{2\pi }{3}$
$sinA=sin\frac{2\pi }{3}=\frac{\sqrt{3}}{2}$