Trigonometry! 40

Geometry Level 4

In $\Delta ABC$ , find $c$ , given $a=5$ , $b=4$ and $\cos (A-B) = \frac {31}{32}$ .

$a$ , $b$ and $c$ are the sides of the triangle opposite to angles $A$ , $B$ and $C$ .

1 solution

Pranav Saxena
Jun 27, 2016

Using cosine rule find cos C. This cos C will be equal to -cos(A+B). Multiply by -1 on both sides to get the value of cos (A+B).

Now add cos(A+B) and cos(A-B). Using the identity, this will be equal to 2cosAcosB Now find cosA and cosB using cosine rule.

Substitute the values. We get an equation involving c^2. That equation is

c^2 = 324/9 c^2 = 36 which implies c = 6 (since length cant be -ve)

Ans.

By any chance is there any shorter method??

Aaghaz Mahajan - 2 years, 2 months ago