You will use GeoGebra to classify triangles by measuring their sides and angles. To get started, open GeoGebra and complete each
step below. If you need help, follow these instructions for using GeoGebra. Question 1 Mark the points (10, 14), (15, 11.11), and (10, 8.22). Enter the coordinates in the input window, if you wish. Then connect the points to form a triangle.
1 answer:
To measure and classify our triangle we are going to perform the following steps:
Step 1. Open GeoGebra or GeoGebra geometry and enter the input of the three points of our triangle.
Step 2. In the measure menu, choose the distance tool and select tow points in our triangle to measure the distance of one side; repeat the process for the other two sides.
Step 3. In the measure menu, choose the angle tool and select three points in our triangle to measure the angle between the three points; repeat the process for the other two angles.
Step 4. After performing the previous steps, we end with a triangle of three equal sides of 5.8 units and three equal angles of 60°. Since all the sides and angles in our triangle are equal, we have an equilateral triangle.
We can conclude that the triangle with coordinates <span>(10, 14), (15, 11.11), and (10, 8.22) is an equilateral triangle.</span>
Step 1. Open GeoGebra or GeoGebra geometry and enter the input of the three points of our triangle.
Step 2. In the measure menu, choose the distance tool and select tow points in our triangle to measure the distance of one side; repeat the process for the other two sides.
Step 3. In the measure menu, choose the angle tool and select three points in our triangle to measure the angle between the three points; repeat the process for the other two angles.
Step 4. After performing the previous steps, we end with a triangle of three equal sides of 5.8 units and three equal angles of 60°. Since all the sides and angles in our triangle are equal, we have an equilateral triangle.
We can conclude that the triangle with coordinates <span>(10, 14), (15, 11.11), and (10, 8.22) is an equilateral triangle.</span>
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Refer to the diagram below. We need to find the areas of the green and blue regions, then subtract to get the area of the orange track only.
The larger green region is composed of a rectangle of dimensions 200 meters by 4+42+4 = 50 meters, along with two semicircles that combine to make a full circle. This circle has radius 25 meters.
The green rectangle has area 200*50 = 10000 square meters. The green semicircles combine to form an area of pi*r^2 = pi*25^2 = 625pi square meters. In total, the full green area is 10000+625pi square meters. I'm leaving things in terms of pi for now. The approximation will come later.
The blue area is the same story, but smaller dimensions. The blue rectangle has dimensions 200 meters by 42 meters, so its area is 200*42 = 8400 square meters. The blue semicircular pieces combine to a circle with area pi*r^2 = pi*21^2 = 441pi square meters. In total, the blue region has area 8400+441pi square meters.
After we figure out the green and blue areas, we subtract to get the orange region's area, which is the area of the track only.
orange area = (green) - (blue)
track area = (10000+625pi) - (8400+441pi)
track area = 10000+625pi - 8400-441pi
track area = (10000-8400) + (625pi - 441pi)
track area = 184pi + 1600 is the exact area in terms of pi
track area = 2178.05304826052 is the approximate area when you use the pi constant built into your calculator. If you use pi = 3.14 instead, then you'll get 2177.76 as the approximate answer. I think its better to use the more accurate version of pi. Of course, be sure to listen/follow your teachers instructions.
