construct triangle PQR in which pq is equal to 5.5cm , qr =8.5cm , and pqr =75°. construct M, the mid point of PR , measure QM
draw PQ of length 5.5
With Q as center draw a circle of radius 8.5
Construct the angle PQR and extend the ray to where it meets the circle. That is R.
Draw PR and construct its perpendicular bisector, which will meet it at M.
Measure QM
I assume you know how to bisect an angle and construct a perpendicular bisector. 75° is 90-15 or 90 - 30°/2
just to check,
QR^2 = (5.5^2 + 8.5^2 - 2*5.5*8.5cos75°) = 78.3
QR = 8.8487
QM = QR/2 = 4.42
Well, to construct the triangle PQR, you'll need to follow these steps:
1. Draw a line segment PQ of length 5.5cm.
2. From point P, draw an angle of 75 degrees with the help of a protractor.
3. On the extended line of PQ, mark a point R at a distance of 8.5cm from Q.
Now, to construct the midpoint M of PR, you can follow the steps below:
4. Draw a line segment PR connecting points P and R.
5. Using a compass, measure the distance between P and R and place the compass at point P.
6. Draw an arc that intersects PR at two points, let's call them A and B.
7. From point B, draw an arc with the same radius as AB, and from point A, draw another arc intersecting the first arc at point M.
8. Draw a line segment QM connecting points Q and M.
And voila! You've constructed the triangle PQR and found the midpoint M. Now, to measure QM, you can use a ruler to measure the length of the line segment QM.
To construct triangle PQR and find the measurement of QM, follow these steps:
Step 1: Draw a line segment PQ of length 5.5 cm.
Step 2: At point P, construct an angle of 75° using a protractor.
Step 3: From point Q, draw a line segment QR of length 8.5 cm that intersects the angle at some point R.
Step 4: Construct the midpoint of line segment PR. To do this, use a compass and draw arcs from points P and R, intersecting at some point M.
Step 5: Connect points Q and M to complete the triangle.
Step 6: Measure the length of line segment QM using a ruler or measuring tape.
Note: To ensure accurate construction, use a ruler and protractor for precise measurements.
To construct triangle PQR, follow these steps:
1. Draw a line segment PQ of length 5.5 cm.
2. At point P, construct an angle of 75 degrees using a protractor.
3. From point Q, draw a line segment QR of length 8.5 cm, forming an angle of 75 degrees with PQ.
4. The intersection point of the lines PQ and QR will be point R.
To construct the midpoint M of PR, follow these steps:
1. Draw a line segment PR connecting points P and R.
2. Use a compass to measure the distance from point P to point R.
3. Open the compass to half the length of PR and draw arcs from both P and R.
4. The intersection point of these arcs will be the midpoint M of PR.
To measure QM, follow these steps:
1. Draw a line segment QM connecting points Q and M.
2. Use a ruler to measure the length of QM.