# How do you find the measure of each of the angles of a triangle given the measurements of the sides are 11, 11, 15?

Jan 20, 2017

Using the Law of Cosines. See explanation for details.

#### Explanation:

First we can use the Law of Cosines to find the angle opposite to the triangle's base (i.e. the longest side):

${15}^{2} = {11}^{2} + {11}^{2} - 2 \cdot 11 \cdot 11 \cdot \cos \beta$

$225 = 121 + 121 - 242 \cos \beta$

$- 242 \cos \beta = 225 - 242$

$\cos \beta = \frac{242 - 225}{242} = \frac{17}{242}$

$\cos \beta \approx 0.0702$

$\beta \approx 85 , {97}^{o}$

To calculate the remaining angles we can use the fact that the triangle is isosceles.

Using this fact we can write that:

$2 \alpha + \beta = 180$

$\alpha = \frac{180 - \beta}{2}$

$\alpha \approx {47.02}^{o}$