Construct a triangle ABC with sides BC = 7 cm, ∠ B = 45° and ∠ A =105°. Then construct a triangle whose sides are times the corresponding sides of Δ ABC.

Question

Construct a triangle ABC with sides BC = 7 cm, ∠ B = 45 ° and ∠ A = 105 ° . Then construct a triangle whose sides are times the corresponding sides of Δ ABC.

Philoid · Accepted Answer

To construct a ΔABC, we first need to find ∠C

We know that,

Sum of angles of a triangle = 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ 105° + 45° + ∠C = 180°

⇒ 150° + ∠C = 180°

⇒ ∠C = 30°

Now, we construct ΔABC

Steps of construction:

1. Draw base BC = 7cm

2. With the help of compass, draw an angle ∠B = 45°

3. With the help of compass, draw ∠C = 30°

4. Mark point A where two rays intersect

∴ ΔABC is the required triangle

Now, we need to make a triangle which is times its size

Steps of construction:

1. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A

2. Mark 4 (the greater of 3 and 4 in ) points B₁, B₂, B₃, B₄ on BX so that BB₁ = B₁B₂ = B₂B₃ = B₃B₄

3. Join B₄C and draw a line through B₃ (the 3^rd point, 3 being smaller of 3 and 4 in ) parallel to B₄C, to intersect BC at C’

4. Draw a line through C’ parallel to the line AC to intersect AB at A’

Thus, A’BC’ is the required triangle.