Answer:
[tex]\frac{25\sqrt{3}}{2}[/tex]
Step-by-step explanation:
The area of a triangle is given by [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] is the base of the triangle and [tex]h[/tex] is the height of the triangle. In a right triangle, the two legs will represent the base and height, both interchangeable.
In a 30-60-90 triangle, the sides are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse of the triangle and [tex]x[/tex] is the side opposite to the 30 degree angle. Since the hypotenuse of this triangle is given as 10, the leg opposite to the 30 degree angle is equal to [tex]10\div 2=5[/tex] and the leg adjacent to the 30 degree angle is equal to [tex]5\sqrt{3}[/tex].
Thus, the area of this triangle is equal to:
[tex]A=\frac{1}{2}\cdot 5\cdot 5\sqrt{3}=\boxed{\frac{25\sqrt{3}}{2}}[/tex]
