Question

Find the BC side of triangle ABC if AB = 5, AC = 6, sinA = √5 / 3 and BC is the largest side of this triangle.

100 points!!!!!!!!

Answer 1

• 10 units (rounded to the whole number)

Explanation:

Given:

• AB = c = 5
• AC = b = 6
• sin A = √5/6
• BC = a = ?

Find the cos A first:

• 
  `cos A = √(1 - sin^2A) =√(1-5/9) =√(4/9)`
• Since a is the greatest side, the angle A is obtuse angle, hence cos A gets negative value
• cos A = - 2/3

Use the law of cosines:

• 
  `a=√(b^2+c^2-2bc*cos A) =√(5^2+6^2+2*5*6*2/3) =√(101) =10.05`