To construct a triangle \(PQR\) with \(PQ = 5.4 \, \text{cm}\), \(P = 100^\circ\), and \(Q = 30^\circ\), follow these steps:
1. Draw a line segment \(PQ\) of length \(5.4 \, \text{cm}\).
2. At point \(P\), use a protractor to measure an angle of \(100^\circ\) counterclockwise. This will give you ray \(PA\).
3. Now, at point \(Q\), measure an angle of \(30^\circ\) counterclockwise. This will give you ray \(QB\).
4. The intersection of \(PA\) and \(QB\) will be point \(R\), completing the triangle \(PQR\).
Ensure that \(QR\) is the longest side, \(PQ\) is the second longest, and \(PR\) is the shortest side. This construction satisfies the given conditions.
Answers & Comments
Answer:
To construct a triangle \(PQR\) with \(PQ = 5.4 \, \text{cm}\), \(P = 100^\circ\), and \(Q = 30^\circ\), follow these steps:
1. Draw a line segment \(PQ\) of length \(5.4 \, \text{cm}\).
2. At point \(P\), use a protractor to measure an angle of \(100^\circ\) counterclockwise. This will give you ray \(PA\).
3. Now, at point \(Q\), measure an angle of \(30^\circ\) counterclockwise. This will give you ray \(QB\).
4. The intersection of \(PA\) and \(QB\) will be point \(R\), completing the triangle \(PQR\).
Ensure that \(QR\) is the longest side, \(PQ\) is the second longest, and \(PR\) is the shortest side. This construction satisfies the given conditions.