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

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:
$= {\tan}^{-} 1 \left(\frac{p e r p}{b a s e}\right) = {\tan}^{-} 1 \left(\frac{8}{15}\right) = {28.0725}^{o}$

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

${180}^{o} - 2 \left({28.0725}^{o}\right) = {123.855}^{o}$