Question 1196262
<font color=black size=3>
This is one way to draw out the diagram
*[illustration triangleDiagram]
Segment CD represents the height of the hut
Let's call it x for now.


Triangle ACD is a 45-45-90 triangle, aka an isosceles right triangle. 
These types of right triangles have congruent legs.
We have CD = x and AD = x as those legs.


AB = 10
DB = AB - AD
DB = 10 - x


Triangle BCD is a 30-60-90 triangle, which means the long leg is exactly {{{sqrt(3)}}} times that of the short leg.
Note the short leg of these types of triangles is always opposite the 30 degree angle. The smallest side is opposite the smallest angle.


So,
{{{long_leg = (short_leg)*sqrt(3)}}}


{{{DB = (CD)*sqrt(3)}}}


{{{10-x = x*sqrt(3)}}}


{{{10 = x*sqrt(3)+x}}}


{{{x*sqrt(3)+x = 10}}}


{{{x(sqrt(3)+1) = 10}}}


{{{x = 10/(sqrt(3)+1)}}} which is one way to express the exact height.
Another way is to rationalize the denominator.


Use a calculator to find that {{{10/(sqrt(3)+1) = 3.66025}}} approximately


Answer: The height is roughly 3.66025 meters


Similar question:
<a href = "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1196263.html">https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1196263.html</a>
</font>