Persevere in solving problems. Create a report that provides a detailed description of the park. Include the following in your report:
the actual side lengths of the triangular plot of land
the type of triangle formed by the intersection of the three streets
the amount of fencing needed to surround the city park
the actual measure of each angle of the triangle
You
Started Monday, December 10th 2018 - 8:49 am
actual side lenths of triangular plot of land: CB = 10 AB = AC = square root 10
3x + 12.5 = 162.5-8
triangle is icosoles.
2.
The centroid of a triangle is the triangle’s center of gravity.
A fountain will be placed at the centroid of the park. The designer wants to place a stone path from the fountain to the midpoint of each side.
a.
Reproduce the diagram in Item 1 showing the location of the fountain and the stone paths. Mark congruent segments on your diagram.
b.
What are the coordinates of the location of the fountain?
c.
What is the actual distance from the fountain to each vertex?
d.
Find the actual length of each stone path.
i have no idea what im doing
need help on number 2 letters a,b,c, and d
sqrt 10 is too short for the equal legs of an isosceles triangle of base 10. Typo?
yea its a typo, its sqrt 74
To answer the questions in your report, we will go through each of them step by step:
1. The actual side lengths of the triangular plot of land:
In your problem, you mentioned that side CB has a length of 10 and sides AB and AC have a length of square root 10. Therefore, the actual side lengths of the triangular plot of land are:
AB = square root 10
AC = square root 10
CB = 10
2. The type of triangle formed by the intersection of the three streets:
To determine the type of triangle, we need to examine the lengths of the sides. Based on the lengths provided in the previous step, we see that AB = AC and CB = AB. This indicates that all three sides are equal. Therefore, the triangle formed is an isosceles triangle.
3. The amount of fencing needed to surround the city park:
To calculate the amount of fencing needed, we need to find the perimeter of the triangular plot of land. The perimeter is simply the sum of the lengths of all three sides. Using the side lengths obtained in step 1, we can calculate the perimeter as follows:
Perimeter = AB + AC + CB
Perimeter = square root 10 + square root 10 + 10
(Some calculations may be needed based on the actual value of square root 10)
Perimeter = (2 * square root 10) + 10
4. The actual measure of each angle of the triangle:
To find the actual measure of each angle in the triangle, we can use the Law of Cosines. The Law of Cosines states that for any triangle with side lengths a, b, and c, and corresponding angle A opposite side a, the following equation holds:
a^2 = b^2 + c^2 - 2bc * cos(A)
In your problem, we know the side lengths but not the angles. To find the angles, we can use the Law of Cosines with different combinations of side lengths and angles.
For example, to find angle A, we can use side lengths AB, AC, and CB:
AB^2 = AC^2 + CB^2 - 2 * AC * CB * cos(A)
We can repeat this process for the other angles by using different combinations of side lengths and angles.
5. Reproducing the diagram and marking congruent segments:
To reproduce the diagram, draw a triangle with sides AB, AC, and CB, as determined in step 1. As for marking the congruent segments, you mentioned that the stone paths are placed from the fountain to the midpoint of each side. Therefore, you can draw segments connecting the fountain to the midpoint of each side and mark them as congruent.
6. Coordinates of the location of the fountain:
To find the coordinates of the location of the fountain, you need additional information about the positions of the vertices of the triangle or any other details about the park. Without more context, it is not possible to provide the coordinates of the fountain.
7. Actual distance from the fountain to each vertex:
Similarly, without additional information or measurements, it is not possible to determine the actual distance from the fountain to each vertex.
8. Actual length of each stone path:
Again, the actual length of each stone path depends on the additional information and measurements that are not provided in the problem. Without more details, it is not possible to calculate the lengths of the stone paths.
In summary, to fully answer all the questions in your report, we need more information or measurements about the park.