Using a ruler and a pair of compasses only, construct triangle ABC such that |AB|=8cm, ABC=90 degree and |BC|=5cm measure AC
To construct triangle ABC with |AB| = 8 cm, ABC = 90 degrees, and |BC| = 5 cm, follow these steps:
1. Draw a straight line segment AB using the ruler, measuring 8 cm in length.
2. Place the compasses' needle on point A and adjust the pencil end of the compasses so that it measures 5 cm.
3. Keeping the compasses at the same width, draw an arc above and below the line segment AB.
4. Without changing the compasses' width, place the compasses' needle on point B and draw arcs that intersect the previously drawn arcs.
5. Label one of the intersection points as C.
6. Using the ruler, draw a line segment between points B and C.
7. Then, using the ruler, draw a line segment between points C and A.
Triangle ABC is now constructed. Measure the line segment AC to find its length.
check:
sqrt ( 8^2 + 5^2) = sqrt (64 + 25) = sqrt (89) = between 9 and 10
You are correct. By applying the Pythagorean theorem, the length of the line segment AC can be found:
√(8^2 + 5^2) = √(64 + 25) = √(89) ≈ 9.4
Therefore, the length of line segment AC is between 9 and 10 cm.
To construct triangle ABC with the given conditions using a ruler and a pair of compasses only, follow these steps:
Step 1: Draw a line segment AB of length 8 cm using the ruler.
Step 2: With point A as the center, draw a circle with a radius of 5 cm using the compass.
Step 3: With point B as the center, draw another circle with a radius of 8 cm using the compass.
Step 4: Label the intersections of the two circles as points C and D.
Step 5: Connect points A and C to create the triangle ABC.
Step 6: Measure the line segment AC using the ruler to get the desired measurement.