A dog walks due east 180 ft to a corner. After turning through an angle of 81.5°,
the dog walks 329 ft. to the second
corner. Then the dog walks back
to the starting point.
What is the area of the triangle
formed by his path?
Area = [?] ft.2
Round to the nearest hundredth.

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

6/20

step-by-step explanation: