the city council is planning a new city park on a triangular plot of land formed by three intersecting streets the designer placed the triangle on a grid to determine the side lengths and angle measures needed for the purchase and placement of a fence surrounding the park each unit on the grid is one inch which represents 20 feet of actual length. THe measure of angle CAB in the designer's diagram is (5x+1) degrees and the measure of angle ACV is (3x+12.5) degrees. What is the actual side lengths of the triangular plot of land?
The next question asks the amount of fencing needed to surround the city park
I got 14 and 37.58
I assume you meant ACB rather than ACV.
Since the angles total to 180, we have for angle ABC,
180-(5x+1)-(3x+12.5) = 162.5-8x
That is all we know. You have given no side lengths, nor even any way to determine the actual angles. Knowing all the angles would not help, since we have no similar triangle to compare against.
The city council is planning a new city park on a triangular plot of land formed by three intersecting streets. The designer placed the triangle on a grid to determine the side lengths and angle measures needed for the purchase and placement of a fence surrounding the park. Each unit on the grid is one inch which represents 20 feet of actual length. THe measure of angle CAB in the designer's diagram is (5x+1) degrees and the measure of angle ACB is (3x+12.5). Angle A is (6.8) Angle B is (11,1) and Angle C is (1,1. What is the actual side lengths of the triangular plot of land?
What is the type of triangle formed by the intersection of the three streets?
well, the side lengths are
CB=10
Note that A is halfway from C to B (6=(1+11)/2), so ABC is an isosceles triangle, and
AB=AC=√74
Now all you have to do is scale up the dimensions by a factor of 20'/1" = 240 to get the actual side lengths.
We weren't asked for the angles, but now it is clear that since ACB=ABC,
(3x+12.5) = 162.5-8x
You can solve for x and figure the actual degree measures.
For the first question I put The actual side length of AB and CA is 8,6 and BC is 10.
For the second question I put the triangle is isosceles because it has two equal sides which are Ab and CA.
Are these the right way to answer these questions?
8.6*
okay so how would we right this out now
how did you get 37.58 and what is the unit for that
The amount of fencing needed to surround the city park
To determine the actual side lengths of the triangular plot of land, we need to find the values of x, which will allow us to calculate the measures of angles CAB and ACV.
Let's start by examining the information given about the grid. The scale for the grid is 1 inch = 20 feet. Therefore, 1 unit on the grid represents 20 feet of actual length.
Now, we know that the triangle is formed by three intersecting streets. Let's label the vertices of the triangle as A, B, and C, with AB and AC being two of the sides.
The measure of angle CAB in the designer's diagram is given as (5x + 1) degrees.
Since AB is one of the sides of the triangle, we can assume it refers to one of the streets. Let's call the length of AB on the grid as a units.
Since 1 unit on the grid represents 20 feet, the length of AB in actual feet would be 20a.
Similarly, the measure of angle ACV in the designer's diagram is given as (3x + 12.5) degrees.
Since AC is another side of the triangle, we can assume it refers to another street. Let's call the length of AC on the grid as b units.
The length of AC in actual feet would be 20b.
Now, we know that the sum of the angles in a triangle is 180 degrees. So we can write the equation:
(5x + 1) + (3x + 12.5) + the measure of angle B = 180
Simplifying, we get:
8x + 13.5 + the measure of angle B = 180
Since the measure of angle B is not given, we can't solve the equation yet. We need more information about angle B or another equation involving x to solve for its value.
Please provide additional information or equations so we can continue solving for the side lengths of the triangular plot of land.