Construct abc in which ab =7cm ac=9.5cm and abc=120 degree measure bc
c = 7
b = 9.5
B = 120 deg
law of cosines
b^2 = a^2 + c*2 - 2 * a * c * cos B
9.5^2 = a^2 + 7*2 - 14 a * -0.5
90.25 = a^2 + 49 + 7 a
a^ + 7 a - 41.25 = 0
a = about 3.81 for positive root
4cm
To construct ABC with the given measurements, we can follow these steps:
Step 1: Draw a line segment AB of length 7 cm.
Step 2: Place the compass at point A and draw an arc with a radius of 9.5 cm. Label the point of intersection with the line AB as point C.
Step 3: With the same compass setting, place the compass at point B and draw an arc intersecting the previously drawn arc. Label the point of intersection as point C.
Step 4: Connect points A and C, and points B and C to form triangle ABC.
Step 5: Measure the angle between line segments AB and BC using a protractor. If the angle measures 120 degrees, then the construction is correct.
Note: Construction steps may vary depending on the tools and techniques used.
To construct triangle ABC, follow these steps:
1. Draw a straight line segment AB measuring 7cm.
2. At point A, draw a ray (half-line) in any direction.
3. Using a compass, set the radius to 9.5cm and draw an arc from point A intersecting the ray. Label the point of intersection as C.
4. Draw a circle centered at point A with a radius of 7cm.
5. Draw a circle centered at point C with a radius of 9.5cm.
6. The two circles should intersect at two points. Label one of the points of intersection as B.
7. Draw a straight line segment connecting points B and C.
8. Measure the angle BAC using a protractor. If it measures 120 degrees, then you have successfully constructed triangle ABC.
Note: If the angle measures differently than 120 degrees, redo the construction starting from step 2, but choose a different direction for the ray in step 2.
By following these steps, you can construct triangle ABC with AB = 7cm, AC = 9.5cm, and angle BAC measuring 120 degrees.