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

$51134

Step-by-step 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=(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 }*141.42\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*\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 }*\text{ \$10,000 per acre = \$5113}4`

Therefore, the land cost $51134