Question

Construct a triangle ABC, given that AB=5cm , ∠ABC=105 ° & ∠BCA=40° .

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• AB = 5 cm

• ∠B = 105°

and

• ∠C = 40°

Let first draw its rough sketch. (See attachment fig. 1)

So,

• In order to draw, ∆ABC

• We first need to find, ∠ A.

We know angle sum property,

• Sum of all the angles of a triangle is 180°.

So,

• In ∆ABC,

We have,

• ⇛ ∠A + ∠B + ∠C = 180°

• ⇛ ∠A + 105° + 40° = 180°

• ⇛ ∠A = 35°

Let's Construct the ∆ABC now!!

Step :- 1 Draw a line segment of AB = 5 cm

Step :- 2 Draw an angle of 35° at point A using protractor.

Step :- 3 Draw an angle of 105° at point B using compass.

Step :- 4 Let point C be the point where lines meet.

Thus, ∆ABC is the required triangle.