Face of the house

How tall is the gable of a house in the shape of an isosceles triangle with a base length of 8 meters and an arm 5 meters long?

Correct answer:

h =  3 m

Step-by-step explanation:

$$\begin{gathered} a=8\text{ m } \\ r=5\text{ m } \\ {r}^2=h^2+(a\mathrm{/}2{)}^2 \\ h=\sqrt{r^2-(a\mathrm{/}2{)}^2}=\sqrt{5^2-(8\mathrm{/}2{)}^2}=3\text{ m} \end{gathered}$$

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