Roof angle

The roof of the house has the shape of an isosceles triangle with arms 4 m long and the size of the base 6 m. How big an angle alpha does its roof make?

Correct answer:

A =  41.4096 °

Step-by-step explanation:

$$\begin{gathered} r=4\text{ m } \\ z=6\text{ m } \\ a=z\mathrm{/}2=6\mathrm{/}2=3\text{ m } \\ \cos A=a:r \\ A={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arccos (a\mathrm{/}r)={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arccos (3\mathrm{/}4)=41.4096\text{°}=41\mathrm{°}24^{\mathrm{\prime }}35\mathrm{"} \end{gathered}$$

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