An isosceles triangle has a height of 8 and base of 30. What are all three angles of this triangle?

1 Answer
Nov 16, 2015

The three angles of triangle are 28.0725^o28.0725o, 28.0725^o28.0725o and 123.855^o123.855o.

Explanation:

An isosceles triangle is symmetric from the centre. If we cut it in half, we will have 2 identical right-triangles with perpendicular=8=8 and base=15=15

To calculate the identical angles opposite to height, we can use trigonometric identities:
=tan^-1 ((perp)/(base))=tan^-1 ((8)/(15))=28.0725^o=tan1(perpbase)=tan1(815)=28.0725o

Third angle can be calculated by subtracting the measure of 2 identical angles from sum of all angles in a triangle i.e. 180^o180o:

180^o-2(28.0725^o)=123.855^o180o2(28.0725o)=123.855o