Question

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

Answer 1

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`