Question

You are buying the triangular plece of land shown. The price of the land is $10,000 per acre (where one acre= 4840 square yards). How much does your place of land cost to the nearest whole dollar

Answer 1

Answer:

$51134

Explanation:

First, we need to find the area of the land. So, we need to identify the height of the triangle h as:

Then, using the trigonometric functions, we can calculate the value of h as:

$\begin{gathered} \sin 45=\frac{\text{Opposite }}{\text{ Hypotenuse}} \\ \sin 45=\frac{h}{200} \\ 200\cdot\sin 45=h \\ 141.42=h \end{gathered}$

Now, the area of the triangle in square yards is:

$\begin{gathered} A=\frac{\text{ Base x Height}}{2} \\ A=\frac{350\text{ yd }\times141.42\text{ yd}}{2} \\ A=24,748.74yd^2 \end{gathered}$

1 acre is equal to 1840 square yards, so the area in acres is:

$24,748.72yd^2\times\frac{1\text{ acre}}{4840\text{ yd}}=5.1134\text{ acres}$

Finally, the price of the land can be calculated as:

$5.1134\text{ acres }\times\text{ \ 10,000 per acre = \ 5113}4$

Therefore, the land cost $51134