Isosceles gable

The roof of a cottage has a gable in the shape of an isosceles triangle with a base length of 8m and a side length of 10m. How high is the gable?

Correct answer:

h =  9.1652 m

Step-by-step explanation:

$$\begin{gathered} a=8\text{m} \\ r=10\text{m} \\ {r}^2=h^2+(a/2{)}^2 \\ h=\sqrt{r^2-(a/2{)}^2}=\sqrt{10^2-(8/2{)}^2}=2\sqrt{21}=9.1652\text{m} \end{gathered}$$

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