constuct two triangles ABC. let the length AB be 5cm and angleC be 54 degrees. find angles A1 and A2.
To construct the two triangles given the length AB and angle C, we can follow these steps:
Step 1: Draw a line segment AB of length 5cm.
Step 2: Place your compass on point A and draw an arc that intersects line AB.
Step 3: Without changing the compass width, place the compass on point B and draw another arc that intersects the previous arc.
Step 4: Label the point of intersection of the two arcs as point C.
Step 5: Draw the line segments AC and BC to complete the two triangles, ABC and A'BC.
Now, let's find the angles A1 and A2:
In triangle ABC:
Angle A + Angle B + Angle C = 180 degrees
Angle A = 180 degrees - Angle B - Angle C
Given that Angle C is 54 degrees, let's assume Angle B is 50 degrees:
Angle A = 180 degrees - 50 degrees - 54 degrees
Angle A = 76 degrees
Therefore, in triangle ABC, Angle A1 is 76 degrees.
Now, for triangle A'BC:
Since angle C is external to triangle A'BC, Angle A2 = Angle C
Angle A2 = 54 degrees
So, in triangle A'BC, Angle A2 is 54 degrees.