MATH SOLVE

4 months ago

Q:
# PLEASE HELP URGENT!!!The price of the land is $2300 per acre ( 1 acre = 4840) how much does the land cost?

Accepted Solution

A:

Two of the three side lengths are given. To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle. Use the Law of Cosines for this task.

a^2 = b^2 + c^2 - 2ac*cosA

Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or

a^2 = 250000 + 572500 - 750000(-0.1736), or

= 692264

Then a = +sqrt(692264) = 832 yds

Use Heron's Formula to find the area of the land.

First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s

According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )

Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )

I will leave this calculation to you to complete.

Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.

In acres, the area is

1 acre

A* ---------------- = (A/4840) acres

4840 yd^2

How much will this cost? Recall that the unit cost of the land is $2300/acre.

Then the total cost will be:

$2300

(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)

1 acre

a^2 = b^2 + c^2 - 2ac*cosA

Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or

a^2 = 250000 + 572500 - 750000(-0.1736), or

= 692264

Then a = +sqrt(692264) = 832 yds

Use Heron's Formula to find the area of the land.

First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s

According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )

Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )

I will leave this calculation to you to complete.

Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.

In acres, the area is

1 acre

A* ---------------- = (A/4840) acres

4840 yd^2

How much will this cost? Recall that the unit cost of the land is $2300/acre.

Then the total cost will be:

$2300

(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)

1 acre