Question

Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.

Answer 1

Step 1: Draw a Ray BX and with B as center and radius 4.8 cm cut an arc on the line and name it as C.

Step 2: With B as center and 3.6 cm as radius draw an arc.

Step 3: With C as center and 3 cm as radius cut the previous arc at A.

Step 4: Join AB and AC.

Our triangle is constructed.

Now we know that the angle opposite to the smallest side is the smallest angle in a triangle.

So ∠ABC is the smallest.

Now bisecting the ∠ABC

Step 5: With B as center draw an arc that cuts AB and BC at P and Q respectively.

Step 6: With P as center and radius more than PQ draw an arc then with Q as center and equal radius draw another arc that cuts the previous arc at Z.

Step 7: Join BZ

Now by cosine rule, we get to know that ∠ABC = 40°

So, ∠ABY = ∠YBC = 20°.