Question

How do you solve the right triangle given a=15,b=11, c=20?

Answer 1

The angles of this triangle are: `A~~51.93`, `B~~28.65`, and `C~~99.42`

Explanation:

This triangle is not right angled one, because it does not satisfy conditions given in Pytagorean Theorem:

`11^2+15^2=121+225=346` and `20^2=400 !=346`.

However you can stil solve this triangle using the Cosine Theorem.

This theorem says that in any triangle following equalities are true:

`c^2=a^2+b^2-2abcosC`

`b^2=a^2+c^2-2accosB`

`a^2=b^2+c^2-2bccosA`

where `A` is the angle opposite to side `a`, `B` is angle opposite to side `b`, and `C` is angle opposite to side `c`.

Using this theorem we can calculate:

`c^2=a^2+b^2-2abcosC`

`20^2=11^2+15^2-2*11*15*cosC`

`400=121+225-330cosC`

`400=346-330cosC`

`54=-330cosC`

`cosC=-54/330`

`C~~99.42deg`

Using similar calculations you can find, that: `A~~51.93`

To calculate `B` you can either use the Law of Cosines again or use the property of any triangle which says that the sum of its angle is equal to 180 degrees.