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

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Answer 1 · 2017-01-20T13:32:54

Using the Law of Cosines. See explanation for details.

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

$15^2=11^2+11^2-2*11*11*cosbeta$

$225=121+121-242cosbeta$

$-242cosbeta=225-242$

$cosbeta=(242-225)/242=17/242$

$cosbeta~~0.0702$

$beta ~~85,97^o$

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

Using this fact we can write that:

$2alpha+beta=180$

$alpha=(180-beta)/2$

$alpha~~47.02^o$