With aim of diagram construct a triangle ABC in which AB=5cm,BC=6cm and angle ABC=120 measure angle ACB,drop a perpendicular from C to cut AB produced at P.Measure CP.
It's easy to construct ABC.
Draw AB of length 5
Construct angle ABC (it's just two adjoining 60° angles)
with center at B, draw a circle of radius 6.
Mark C where the circle intersects ray BC.
So now produce AB to P and construct a ⊥ from C to P.
Measure CP
To confirm your answer, it is clear that angle BCP = 60°
So CP = 6 sin60° = 3√3
Excellent
To construct the triangle ABC, follow these steps:
Step 1: Draw a straight line segment AB of length 5 cm using a ruler.
Step 2: Place the tip of the compass on point A and draw an arc with a radius of 6 cm to intersect the line segment AB. Label the point of intersection as C.
Step 3: Keeping the compass radius the same, place the tip on point C and draw an arc to intersect the previously drawn arc. Label this point as B.
Step 4: Draw a line segment BC to connect points B and C using a ruler.
Step 5: Measure the angle ABC using a protractor and verify that it measures 120 degrees.
To find the measure of angle ACB and the length of CP, follow these steps:
Step 6: Draw a line segment CP perpendicular to AB. This can be done by placing the compass tip on point C and drawing two arcs, intersecting AB and forming an X. Connect the points of intersection to create the perpendicular line.
Step 7: Measure the angle ACB using a protractor and record its measure.
Step 8: Measure the length of CP using a ruler.