Question

An equilateral triangle has a height of 10 feet. How long is one of its sides? (Note: In an equilateral triangle, all sides have the same length.)

Answer 1

Answer:

side length is $\frac{20\sqrt{3} }{3}$ feet

Step-by-step explanation:

An equilateral triangle has a height of 10 feet.  the height of the triangle is the perpendicular bisector to the base

so it forms a two right angle triangle

the triangle formed is a 30-60-90 degree triangle

the diagram is attached below

Let x be the side if the equilateral triangle

sin(theta)=opposite by hypotenuse

$sin(60)=\frac{10}{x}$

$\frac{\sqrt{3}}{2} =\frac{10}{x}$

cross multiply

$\sqrt{3} x=20$

$x=\frac{20}{\sqrt{3} } =\frac{20\sqrt{3} }{3}$