how do we draw a triangle with two of the angels 40 degrees and 120 degrees and circumradius 3 centimeters ?
start with a sketch of the finished product
Let the triangle be ABC, so that angle B = 120°,
angle BCA = 40° and angle CAB = 180-40-120 = 20°
the centre of the triangle, O, lies on the right-bisectors of BC and AB, so that
CO = AO = BO = 3 cm
remember that the central angle of a chord is twice the angle subtended by the same chord at the circle
so angle BOA = 80° and angle COB = 40° making angle COA = 120°
also in triangle COA, which is isosceles,
angle ACO = angle COA = 30°
all angles can be found.
So I would start by drawing a circle with radius 3 cm
Pick any point C,
Using your protractor , draw angle OCB = 70°, where B is the point on the circle
Using your protractor, draw angle COA = 120°, with A on the circle.
Depending on your accuracy of the protractor and your skill, triangle ABC is your required triangle.
NOTE: since you are using actual measurements, this is not the traditional straight-edge and compass construction.
To draw a triangle with two angles measuring 40 degrees and 120 degrees and a circumradius of 3 centimeters, you can follow these steps:
Step 1: Draw a straight line segment with a length of 6 centimeters and label it as AB. This line segment will be the base of the triangle.
Step 2: Place the compass at point A and set it to a radius of 3 centimeters, which is the given circumradius.
Step 3: Draw an arc from point A, intersecting line AB, and label the point of intersection as C.
Step 4: Place the compass at point C and set it to a radius of 3 centimeters.
Step 5: Draw an arc with the compass intersecting line AB, and label the point of intersection as D.
Step 6: Connect points A and D to form one side of the triangle.
Step 7: Connect points B and D to form another side of the triangle.
Step 8: Finally, connect points A and B to close the triangle.
Following these steps will help you draw a triangle with the given angles and circumradius.
To draw a triangle with two angles measuring 40 degrees and 120 degrees, along with a circumradius of 3 centimeters, follow these steps:
Step 1: Begin by drawing a straight line segment of length 6 centimeters (twice the circumradius) on a paper using a ruler. This line will represent the diameter of the circumcircle.
Step 2: On one end of the line segment, place your compass and draw an arc with a radius of 3 centimeters, ensuring that the arc intersects the line segment.
Step 3: Without changing the compass width, place the compass point at the other end of the line segment and draw another arc, intersecting the line segment and the first arc you drew.
Step 4: The two intersection points on the line segment are the base vertices of your triangle.
Step 5: From one base vertex, draw a straight line segment connecting it to the center of the circumcircle (midpoint of your line segment).
Step 6: At the other base vertex, draw a straight line segment that intersects the point where the circumference of the circle intersects the line segment. This will form the third vertex of your triangle.
Step 7: Label the three vertices of your triangle.
Step 8: Now you have a triangle with two angles measuring 40 degrees and 120 degrees, along with a circumradius of 3 centimeters.