Answer:
96√3 m²
Step-by-step explanation:
Triangle ABC is a 30-60-90 triangle.
This is a special right triangle where the measures of its sides are in proportion [tex]x:x\sqrt{3}:2x[/tex]:
- x is the side opposite the 30° angle
- x√3 is the side opposite the 60° angle.
- 2x is the side opposite the right angle.
The side opposite the 30° angle is the height of the triangle.
The side opposite the 60° angle is the base of the triangle and is 24 m.
Therefore, find x:
[tex]\implies x\sqrt{3}=24\\\\ \implies x=\dfrac{24}{\sqrt{3}}\\\\ \implies x=8\sqrt{3}[/tex]
Therefore:
- Base of the triangle = 24 m
- Height of the triangle = 8√3 m
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height. \\\end{minipage}}[/tex]
Substitute the found base and height into the formula and solve for area:
[tex]\implies A=\dfrac{1}{2} \cdot 24 \cdot 8\sqrt{3}[/tex]
[tex]\implies A=12 \cdot 8\sqrt{3}[/tex]
[tex]\implies A=96\sqrt{3}\;\; \sf m^2[/tex]
Therefore, the exact area of the triangle is 96√3 m².
