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)°, and the
measure of angle acb is (3x + 12.5)°.

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

Step-by-step explanation:

The actual side lengths of the triangular plot of land:

The length of AC = inches

The length of AB = inches

The length of CB = 11 inches - 1 inch = 10 inches

The type of triangle formed by the intersection of the three streets:

Since AC = AB , the triangle ACB is an isosceles triangle.

Actual measure of each angle of the triangle:

∠ACB = ∠ABC = 3x + 12.5 = 3x + 12.5 (isosceles triangle has two equal angles)

(5x + 1)° + 2(3x  + 12.5)° = 180° (angles in a triangle adds up to 180°)

5x + 6x + 1 + 25 = 180°

11x = 154

x = 14

∠CAB = (5(14) + 1)° = 71°

∠ACB = ∠ABC = 3(14) + 12.5 = 54.5°

The actual side lengths of the triangular plot of land:

Given; 1 inch = 20 feet

CB = 10 inches = 200 feet

i.e

AB = AC = ( 200 × sin 54.5°) ÷ sin 71° = 172.2 feet (correct to one decimal place)

The amount of fencing needed to surround the city park

:

The perimeter of the city pack = CB + AB + AC = 200 feet + 2(172.2) feet = 544.4 feet

Look at the tenths place to round to the nearest whole number.

Compare the estimated sum to the actual sum.

The estimated answer is close to the actual answer.

Step-by-step explanation:

Sample respond :)