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

1 Answer
Kashan Hanif
Nov 16, 2015

The three angles of triangle are #28.0725^o#, #28.0725^o# and #123.855^o#.

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# and base#=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#

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

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

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