# Ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles

The ratio of an isosceles triangle to its altitude is 3:4. find the measures of the angles of triangle? So, I have the altitude formula where $h$= $\sqrt s^2-(\frac{s}{2})^2$ so I was thinking when I have the altitude the triangle will be into $2$ right triangles and I think I need to get the sides first then derive the formula for Area which is $A$=$\frac{1}{2}$ $absin$ but I'm confuse on how to get the sides if it only says base is $3:4$ to its altitude

• When you say, “ratio of an isosceles triangle to its altitude”, are you talking about the base of the triangle versus the altitude? If so, could you edit? Nov 21, 2014 at 14:16

## 1 Answer

Notice you need only the angle (which is a ratio). We have that the ratio of the base to its altitude is $3:4$. Then the ration of half the base to its altitude is $3:8$. This ratio is the cotangent of the angle at the base. If we have the cotangent we have the angle.