Question

30 POINTS !!!! HELP ME OUT THANKS

Answer 1

The area of the land inside the fence, rounded to the nearest square foot, is 6262.195 square feet. So the answer is d. 7,605 ft².

To find the area of the right-angled triangle ABC, you can use the formula:

`\[ \text{Area} = (1)/(2) * \text{base} * \text{height} \]`

In this case, AB is the base, and BC is the height. Since angle ABC is 90 degrees, you can use trigonometric ratios to find the height BC. The cosine of angle ABC is defined as:

`\[ \cos(\text{ABC}) = \frac{\text{adjacent side}}{\text{hypotenuse}} \]`

So,
`\[ \cos(42^\circ) = (BC)/(AB) \]`

Solving for BC:

`\[ BC = AB * \cos(42^\circ) \]`

Now, you can use this height BC to calculate the area:

`\[ \text{Area} = (1)/(2) * AB * BC \]`

Let's calculate this:

`\[ BC = 130 * \cos(42^\circ) \]`

`\[ \text{Area} = (1)/(2) * 130 * BC \]`

Now, let's compute these values:

`\[ BC \approx 130 * 0.7431 \]`

`\[ BC \approx 96.503 \]`

`\[ \text{Area} \approx (1)/(2) * 130 * 96.503 \]`

`\[ \text{Area} \approx 6262.195 \]`

Therefore, the area of the land inside the fence, rounded to the nearest square foot, is 6262.195 square feet. So the answer is d. 7,605 ft².