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S.1 EXERCISE 2 - 2021. 1. (a) Using a ruler and a pair of compasses only, construct a triangle ABC in which AB = 5-6cm, BC = 6-2cm and angle ABC=135º. Measure length AC and angle BCA. (b) Draw a perpendicular from C to meet AB produced at D. (c) Construct a circle circumscribing triangle BCD and state its radius. (d) Calculate the area of the segments cut off by triangle BCD.



Answer :

Step of construction

AB = 5.6 cm

BC = 6.2 cm

(a)

1. Draw a line segment AB = 5.6 cm

2. At B, draw a ray making an angle of 135°

3. Draw line segment for BC = 6.2 cm

4. Join AC

Measure length AC and angle BCA

Obtuse Scalene Triangle

AB = 5.6cm

BC = 6.2cm

AC = 10.9cm

°

(b) Draw a perpendicular from C to meet B

(c) Construct a circle circumscribing triangle BCD

Radius would be equal to r = 5 cm

(d) Area of BCD

BD = 5.6/2 = 2.8cm

h = BC*sin(45) = 6.2*sin(45) = 4.38cm

A = BD*h/2 = 2.8*4.38/2 = 6.13cm^2

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