# If a triangle has sides of length 8cm, 8cm, and 5cm, how do I find the measure of the angle between the two equal sides?

Nov 15, 2015

Use the cosine rule to find the angle as $36 , {42}^{\circ}$.

#### Explanation:

The cosine rule states that for a triangle of sides $a , b , \mathmr{and} c$, and with angle $\theta$ opposite side $a$, the following relationship holds :

${a}^{2} = {b}^{2} + {c}^{2} - 2 b c \cos \theta$.

Applying this rule to the given problem yields :

${5}^{2} = {8}^{2} + {8}^{2} - 2 \cdot 8 \cdot 8 \cdot \cos \theta$

$\therefore \theta = {\cos}^{- 1} \left(\frac{25 - 2 \cdot 64}{- 128}\right) = 36 , {42}^{\circ}$.