Answer :
The area of triangle ABC is approximately 1190.25 square feet. To find the area of triangle ABC, we can use the formula for the area of a triangle: A = 1/2 * base * height.
Step 1: Find the height of the triangle.
We can use the Law of Sines to find the height. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In this case, we have angle C and sides a and b.
First, we find the third angle of the triangle:
Angle A + Angle B + Angle C = 180°
Angle A + 90° + 134.9° = 180°
Angle A = 180° - 90° - 134.9°
Angle A = 45.1°
Now, we can use the Law of Sines to find the height:
sin(45.1°) / 47.8ft = sin(134.9°) / h
h = (47.8ft * sin(134.9°)) / sin(45.1°)
h ≈ 62.47ft
Step 2: Calculate the area of the triangle.
Using the formula A = 1/2 * base * height, where the base is side b and the height is h:
A = 1/2 * 38.2ft * 62.47ft
A ≈ 1190.25ft²
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