A dog walks due east 180 ft to a corner.
1 answer:
Answer:
Area = 29284.87 ft²
Step-by-step explanation:
I've drawn a triangle to depict the movement of the dog with the angle and dimensions.
From the attached triangle, we see that the starting point is C, the first point is A and the second point is B.
Let's find the third side from the image using law of cosine.
Thus;
b² = a² + c² - 2ac cos B
Thus;
b² = 180² + 329² - 2(180 × 329)cos 81.5
b² = 32400 + 108241 - 17506.55
b² = 123134.45
b = √123134.45
b = 350.91 ft
We calculate the area of the triangle using heron's formula.
Area = √(p(p − a)(p − b)(p − c))
Where p = (a + b + c)/2 = (180 + 350.91 + 329)/2 = 429.955 ft
Area = √(429.955(429.955 - 180)(429.955 - 350.91)(429.955 - 329)
Area = 29284.886 ft²
To the nearest Hundredth gives;
Area = 29284.87 ft²
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