Finding an angle when three sides are given

[King E]

Consider a ΔABC.

The three sides given are:

AB = 8cm

AC = 15cm

BC = 17cm

The angle required is ∠A.

If I apply Pythagoras theorem, that is BC² = AB² + AC² in this case, then I come to know that it is a right angle.



Is there a way to find ∠A without using the Pythagoras theorem BC² = AB² + AC² ?

 

[Deleted member 4993]

Have you learned Law of Cosines of a triangle?

 

[Steven G]

You can also use Heron's formula to find the area and hence the length AD. Then you can find the two angles which make up <A.

 

[blamocur]

Once you know the triangle's area you can figure out sin(A) without analyzing the "sub-angles" (https://www.cuemath.com/measurement/area-of-triangle/)

 

[Steven G]

Once you know the triangle's area you can figure out sin(A) without analyzing the "sub-angles" (https://www.cuemath.com/measurement/area-of-triangle/)

Yeah, yeah you're right. Having the line AD steering me in the face made me make my comment.