Q2 of 4 Page 213

Let’s construct a triangle whose length of two sides are 6cm. and 9cm. and the measurement of the angle opposite to the side of length 9cm. is 105°. Let’s write for what length of sides we will not be able to construct two triangle.

Let the triangle be ΔABC with AB = 6 cm and BC = 9 cm


Now angle opposite to side with length 9 cm that is angle opposite to side BC is ∠A which is 105°


So if we draw it roughly it will look like



Let us construct the triangle now


Step1: Construct AB of length 6 cm



Step2: As ∠A = 105° but we don’t know the length of AC so we will just draw a ray at angle 105°



Step3: As BC is 9 cm we will take 9 cm in compass, keeping the needle of compass on point B mark an arc intersecting the ray drawn in step 2 at point C.



Step4: Join BC and using scale measure the unknown length AC



So we get AC = 5.3 cm now if AC is greater than or less than 5.3 cm then length of BC will also change and hence we cannot construct the given triangle if AC is greater or less than 5.3 cm


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