Answer:
[tex]V=5\sqrt{3}\ m^3[/tex]
Step-by-step explanation:
we know that
The volume of a trough is equal to
[tex]V=BL[/tex]
where
B is the area of equilateral triangle
L is the length of a trough
step 1
Find the area of equilateral triangle B
The area of a equilateral triangle applying the law of sines is equal to
[tex]B=\frac{1}{2} b^{2} sin(60\°)[/tex]
where
[tex]b=2\ m[/tex]
[tex]sin(60\°)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]B=\frac{1}{2}(2)^{2} (\frac{\sqrt{3}}{2})[/tex]
[tex]B=\sqrt{3}\ m^{2}[/tex]
step 2
Find the volume of a trough
[tex]V=BL[/tex]
we have
[tex]B=\sqrt{3}\ m^{2}[/tex]
[tex]L=5\ m[/tex]
substitute
[tex]V=(\sqrt{3})(5)[/tex]
[tex]V=5\sqrt{3}\ m^3[/tex]
