Answer:
55.4 ft²
Explanation:
The special triangle with angles 30°-60°-90° has side lengths in the ratios ...
1 : √3 : 2
The area of the triangle can be found using the area formula ...
A = 1/2bh
where b is the base and h is the perpendicular height.
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sides
The longest side is given as 16 ft. This corresponds to "2" in the ratio, so the other two sides have lengths ...
8 ft, 8√3 ft
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area
These area the perpendicular sides of the triangle so, work well to find the area.
A = 1/2bh
A = 1/2(8√3 ft)(8 ft) = 32√3 ft²
A ≈ 55.4 ft²
The area of the triangle is about 55.4 square feet.