Question

Using a ruler and a pair of compasses only, construct triangle ABC such that |AB|=8cm, ABC=90 degree and |BC|=5cm measure AC

Answers

Answered by Damon
check:
sqrt ( 8^2 + 5^2) = sqrt (64 + 25) = sqrt (89) = between 9 and 10
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.

Related Questions