Q1 of 59 Page 65

Construct a triangle ABC, in which AB = 4.5 cm, AC = 5.5 cm and ∠BAC = 75°.

We have been given two sides and one angle of triangle ABC.

Steps of construction for this case would be:


1. Draw a line segment sufficiently long using a ruler.



2. Locate points A and B such that AB = 4.5 cm on the line segment so formed in the previous step.



3. At A, construct a line segment AX, sufficiently large, such that ∠XAB = 75°; use protractor to measure the angle 75°.



4. With A as centre and radius 5.5 cm, draw a circle or semicircle or an arc cutting the line segment AX at C using a compass and a ruler.



5. Join BC using a ruler.



Thus, ABC is the required triangle.


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