Question

Using a pair of compass only, construct a triangle ABC such that AB = 9cm, angle BAC = 60°, and angle ABC = 45°. Measure the sides AC and BC.

Answer 1

Construct triangle ABC with AB as 9cm, angle BAC as 60 degrees, and angle ABC as 45 degrees using a compass. Measure sides AC and BC directly from the constructed triangle. Use trigonometric relationships to validate the measured sides.

Step-by-step explanation:

To construct a triangle ABC with given measurements using only a pair of compasses, follow these steps:

1. Draw a base line AB that is 9cm long.
2. At point A, construct a 60° angle using the compasses. This is done by opening the compass to any radius, drawing an arc that crosses AB, and then without changing the radius, drawing an arc from where the first arc crossed AB. From point A, draw a line that passes through the intersection of the two arcs; this line makes a 60° angle with AB.
3. At point B, construct a 45° angle. Similar to step 2, this involves drawing two arcs and a line that passes through their intersection. This line will intersect with the line from step 2.
4. Label the point of intersection as point C. Triangle ABC should now be formed with the given angles at A and B.
5. To find AC and BC, use the compasses to measure the sides directly from the drawing.

Note that the exact lengths of AC and BC can only be determined by constructing and measuring the triangle as described, not through a predefined theoretical method. After measuring, you can check the triangle's validity using the Pythagorean theorem and trigonometric relationships.