a concrete border is to be built around a traingular flower garden that has sides of 10m , 7m and 8m. the border is to be staight walking path 1m wide on all sides of the garden. before the concrete can be poured, wooden forms need to be placed on the inside perimeter and on the outside perimeter of the border. determine the totallength of wood needed to build the forms.


ps- i understand other people already answered this question but i havent learned that yet, what i need to use is like the cosine law and sine law and stuff, is there anyway to do it like that, if not can u please explain in detail how to do it( EXTREMELY IMPORTANT PLZ AND TY)

I used both the sine law and the cosine law in the solution that I provided for you in your earlier post of this same question.

I thought the steps that I showed you were about as detailed as I could in this format.

btw, here is the previous post

http://www.jiskha.com/display.cgi?id=1244593158

To determine the total length of wood needed to build the forms for the concrete border around the triangular flower garden, you can use the cosine law and sine law to calculate the lengths of various sides and angles of the triangle.

Let's start by labeling the sides of the triangle:
- Side a = 10m
- Side b = 7m
- Side c = 8m

To find the angles of the triangle, you can use the cosine law:

cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)
cos(B) = (a^2 + c^2 - b^2) / (2 * a * c)
cos(C) = (a^2 + b^2 - c^2) / (2 * a * b)

Now, let's calculate the angles A, B, and C:

cos(A) = (7^2 + 8^2 - 10^2) / (2 * 7 * 8)
cos(A) = (49 + 64 - 100) / 112
cos(A) = 13 / 112
A = cos^(-1)(13 / 112)

cos(B) = (10^2 + 8^2 - 7^2) / (2 * 10 * 8)
cos(B) = (100 + 64 - 49) / 160
cos(B) = 115 / 160
B = cos^(-1)(115 / 160)

cos(C) = (10^2 + 7^2 - 8^2) / (2 * 10 * 7)
cos(C) = (100 + 49 - 64) / 140
cos(C) = 85 / 140
C = cos^(-1)(85 / 140)

With these angles calculated, you can now find the lengths of the sides of the walking path.

To find the length of the side (d) opposite angle A, you can use the sine law:

sin(A) / a = sin(d) / d
d = (sin(A) * a) / sin(d)

Similarly, you can find the lengths of the sides (e and f) opposite angles B and C, respectively.

d = (sin(A) * a) / sin(A + B)
e = (sin(B) * b) / sin(C + B)
f = (sin(C) * c) / sin(A + C)

Finally, calculate the total length of wood needed by adding the lengths of all three sides (d, e, and f) along with the measurements of the garden sides (a, b, and c):

Total length of wood = (d + e + f) + 2(a + b + c)

Note: Make sure to convert the angles to radians before performing any trigonometric calculations.

To determine the total length of wood needed to build the forms, we will first calculate the perimeter of the triangular flower garden, and then add the lengths required for the walking path on all sides.

Let's start by calculating the perimeter of the triangular flower garden. The perimeter of any polygon is found by summing the lengths of all its sides.

Given that the sides of the triangular garden are 10m, 7m, and 8m, the perimeter would be:

Perimeter = 10m + 7m + 8m
Perimeter = 25m

Now let's calculate the total length of the wood needed for the entire form, including the path.

Since the walking path is 1m wide on all sides, we need to extend the sides of the garden by 1m. This means we need to add 1m to each side.

To extend each side, we can use the concept of similar triangles. For each side of the triangular garden, we can form a similar triangle by extending the side by 1m. The ratio of the lengths of the corresponding sides of the similar triangles will be the same.

Let's calculate the extended length of each side:

10m + 1m = 11m (extended length of the longest side)
7m + 1m = 8m (extended length of one of the shorter sides)
8m + 1m = 9m (extended length of the remaining side)

Now, we have the lengths of the extended triangle formed by the walking path. To calculate the total length of wood needed for the inside perimeter, we add up all the sides of the extended triangle:

Inside Perimeter = 11m + 8m + 9m
Inside Perimeter = 28m

Next, we need to calculate the outside perimeter of the form, which includes the outside edge of the walking path. We can calculate this by adding 2 times the width of the walking path to each side:

Outside Perimeter = (10m + 2*1m) + (7m + 2*1m) + (8m + 2*1m)
Outside Perimeter = 13m + 9m + 10m
Outside Perimeter = 32m

Finally, to calculate the total length of wood needed, we add the lengths of the inside and outside perimeters:

Total Length of Wood Needed = Inside Perimeter + Outside Perimeter
Total Length of Wood Needed = 28m + 32m
Total Length of Wood Needed = 60m

Therefore, to build the forms, a total of 60 meters of wood will be needed.