Using ruler and compasses only, construct a triangle ABC having given angle ABC = 60^o, angle ACB = 45^o and the perpendicular from vertex A to BC equal to 2.5cm. Measure AB. Plz explain with steps..........

Given, ∠B = 60° and ∠C = 45°.

Using angle sum property of triangle, we have

∠B + ∠C + ∠A  = 180°

⇒ 60° + 45° + ∠A  = 180°

⇒ ∠A  = 75°

Steps of Construction:

1) Draw a line BX.

2) Place the compass on point B and draw an angle of 60° as shown.

3) Now, open the arc of compass equivalent to 2.5 cm and from point B and from any other point on BX draw an arc at R and S as shown.

4) Join R and S. Now,PQ is a line parallel to BX at an height of 2.5 cm from it.

5) The point where line BY and PQ meet each other is the point A. 

6) From point A, take the angular bisector of 60° and 120° and draw an angle of 90° as shown by dotted line AZ.

7) Again,take the angular bisector of of 60° and 90° and draw an angle of 75°as shown.

8) Now, the point at which it cuts the BX is the required point C. 

9)  Hence, triangle ABC is the required triangle.

Try to  measure AB yourself with the help of ruler after constructing the same.