construct a triangle ABC such that AB=12cm,AC=8cm and <BAC=30°.Draw a perpendicular line from C to meet AB at M.Measure <ABC,CM.Calculate the area of ∆ABC
constructing the triangle should be no problem.
many examples of angle construction online.
since 30° is one of those special angles, the area is easy to calculate. Using the usual labeling, with angles A,B,C and sides a,b,c we have
area = 1/2 bc sinA = 1/2 * 12 * 8 * 1/2 = 24
use the law of cosines to find BC
then use the law of sines to find angle B
If you haven't had trig yet, then just construct and measure as instructed ...
To construct triangle ABC, you'll need a compass and a ruler. Here are the step-by-step instructions:
1. Draw a straight line segment AB of length 12 cm.
2. At point A, use the compass to draw an arc with a radius of 8 cm.
3. At point B, use the compass to draw another arc with a radius of 12 cm, intersecting the previous arc.
4. Let the intersection point be C.
5. Draw a line segment AC.
6. Measure the angle BAC with a protractor and verify that it equals 30°.
7. Draw a perpendicular line from point C to line AB.
8. Let the intersection point be M.
9. Measure the angles of triangle ABC using a protractor to find the value of angle ABC.
10. Measure the length of line segment CM using a ruler.
To calculate the area of triangle ABC with the given measurements, you can use the formula:
Area = (1/2) * base * height
In this case, the base is AB, which has a length of 12 cm. To find the height, you can use the length of CM.
Note: To measure the angles and length accurately, use a protractor and ruler.
To construct triangle ABC and find the measurement of angles and the area, follow these steps:
1. Draw a straight line segment AB of length 12 cm.
2. Using a compass, set the width to 8 cm. Place the compass at point A and draw an arc, intersecting the line AB at point C.
3. Now, draw a line segment AC connecting points A and C.
4. Angle BAC is already specified as 30 degrees.
5. Construct the perpendicular line from point C to line AB. To do this, draw an arc from point C that intersects both sides of angle BAC. Label the point where the arc intersects AB as M.
(Note: The perpendicular line drawn from C to AB creates a right angle, as angle BAC is 30 degrees.)
To find the measurement of angle ABC:
6. Without changing the compass width, place the compass at point B and draw an arc that intersects line AC. Label the point of intersection as D.
7. Draw a straight line segment BD.
8. Angle ABC is equivalent to angle BDC.
To calculate the area of triangle ABC:
9. Label the base of the triangle as AB (12 cm) and the height as MC.
10. For triangle ABC, the area formula is given by:
Area = 0.5 * base * height.
Substitute the values: Area = 0.5 * 12 cm * MC.
Now, measuring the angles and calculating the area:
11. Use a protractor to measure the angle ABC (angle BDC). Place the protractor with its center at point B and the base along line BD.
12. Read the angle measurement in degrees.
To calculate the length of CM:
13. Measure the line segment MC using a ruler.
With these measurements, you can now calculate the area of triangle ABC using the formula mentioned earlier.