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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

Mickey
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  • 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? – Lubin Nov 21 '14 at 14:16

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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.