Construct triangle P Q R such that /P Q/= 4cm /Q R/= 3cm /P R/= 5cm.
Measure :
a) Angle P Q R.
b) Angle P R Q.
c) Angle QPR.
this is a 3-4-5 right triangle ... Q is the right angle
tanR = QP/QR = 4/3
R = 53°
P = 90° - R = 37°
To construct triangle PQR, we will use the given measurements of the sides. Here are the steps to construct the triangle:
1. Draw a straight line segment PQ of length 4cm. This will be one side of the triangle.
2. From the endpoint of PQ, P, draw another line segment PR of length 5cm. Ensure that PR is not collinear with PQ.
3. Now, draw a circle with center P and radius 3cm. This can be done by placing the point of the compass at P, opening it to a distance of 3cm, and drawing an arc intersecting PR.
4. From the intersection point of the circle and PR, mark it as point Q.
5. Connect points Q and R to complete the triangle PQR.
Now, let's find the measures of the angles of triangle PQR:
a) Angle PQR:
To measure angle PQR, you can use a protractor. Place the protractor on the line segment QR such that the center of the protractor coincides with point Q. Then, read the angle measure where the line segment PQ intersects the protractor. This will give you the measure of angle PQR.
b) Angle PRQ:
To measure angle PRQ, again, place the protractor on the line segment PQ such that the center of the protractor coincides with point R. Then, read the angle measure where the line segment QR intersects the protractor. This will give you the measure of angle PRQ.
c) Angle QPR:
To measure angle QPR, place the protractor on the line segment PR such that the center of the protractor coincides with point P. Then, read the angle measure where the line segment RQ intersects the protractor. This will give you the measure of angle QPR.