Construction of a triangle ΔABC where BC=7cm, ∠B=75° and AB+AC=13cm.

Explore how a triangle can be constructed
with given base-length, one base angle and
the sum of other two sides. You can also see how, with a compass,
60°, 120°, 90°, and 75° angles are drawn in the animation.

How to Construct a ΔABC where BC=7cm, ∠B=75° and AB+AC=13cm.

* Draw a base BC = 7cm.
* Draw segment BY so that ∠CBY = 75°.

How to draw a 75° angle»

* To draw a 75° angle, we need to draw a 60° and a 90° angle.
* To draw a 90° angle, we need to draw a 60° and a 120° angle.
* First we draw the 60° and 120° angle.
* In between 60° and 120° angles, another 60° angle is created.
* Bisecting this angle we get the 90° angle(60 + 60 / 2).
* In between 60° and 90° angles, a 30° angle is created.
* Bisecting this angle we get the 75° angle(60 + 30 / 2).

* Put point D on line BY so that BD=13 cm
* Join CD
* Draw a perpendicular bisector PQ on CD
* Let PQ intersect BD at point A.
* Join AC to get the required triangle ABC