Using a ruler and a pair of compasses only construct
Triangle abc such that ab=4.5cm ac=6cm and bac = 30
I would construct an equilateral triangle, which would give me a 60° angle
(easy to do: just draw a suitable base length, set your compass equal to
that base length, draw arcs above from both ends of the base, connect the ends of the base line to the intersection of the arcs. You have constructed a triangle with 3 equal sides, so the angles are all equal to 60° )
Now bisect that 60° angle, then construct sides of 4.5 cm and 6 cm of the
sides asked for. And there you have it!!
Construction
1. Draw a line segment AB of length 4.5 cm.
2. Draw a circle with center A and radius 6 cm. This circle intersects AB at a point C.
3. Join AC and BC to form triangle ABC.
4. To construct the 30 degree angle at A, draw a line from A perpendicular to AB and mark the midpoint D of AB.
5. Using the compass, draw an arc centered at D with radius AB.
6. With the same radius, draw another arc centered at A intersecting the first arc at point E.
7. Draw a line from A to E. This forms a 30 degree angle at A.
8. Label the intersection of BC and AE as point F.
9. Triangle ABC is now constructed with sides AB = 4.5 cm, AC = 6 cm, and angle BAC = 30 degrees.
Well, building triangles with a ruler and a pair of compasses can be quite the challenge, especially without drawing any funny faces on them! But fear not, because I'm here to assist you with a humorous solution!
First, let's take out our trusty ruler and draw a line segment AB measuring 4.5cm. Feel free to imagine the ruler with a hilarious clown face if that helps you stay entertained during this process!
Next, use your uproariously funny pair of compasses and set the width carefully to 6cm. Place the compass point on the endpoint A of the line segment AB and draw an arc that intersects the line segment AB. This will give you a point, let's call it C, somewhere on the line segment.
Now, using your uncontrollably funny pair of compasses, set the width again to match the length of AB. Place the compass point on the point C and draw an arc that intersects the arc you drew previously. Let's call the point of intersection between the two arcs, B.
Congratulations, you've constructed a triangle, affectionately named ABC! And guess what? This triangle has sides AB = 4.5cm, AC = 6cm, and angle BAC = 30 degrees!
Now, sit back and enjoy a hearty laugh because you've successfully constructed a triangle using nothing but a ruler, a pair of compasses, and a sprinkle of humor!
To construct triangle ABC with the given dimensions using only a ruler and a pair of compasses, follow these steps:
1. Draw a line segment AB of length 4.5 cm using the ruler. This will be the base of the triangle.
2. Open the compasses to a width of 6 cm. Place the sharp end of the compass at point A and draw an arc above AB. Label the intersection of the arc with the line as point C.
3. With the same width on the compasses, place the sharp end on point C and draw another arc that intersects the first arc. Label this intersection point as B.
4. Now, use the ruler to draw a line segment from point C to point B. This will complete triangle ABC.
5. To verify that the angle BAC is 30 degrees, you can measure it using a protractor.
Now, you have successfully constructed triangle ABC with sides AB = 4.5 cm, AC = 6 cm, and angle BAC = 30 degrees using only a ruler and a pair of compasses.