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Construction Of Triangles

Class 8th Mathematics West Bengal Board Solution
Lets Do 21.1
  1. Let's draw a triangle whose two angles are of measurements 45° and 30° and length of…
Lets Do 21.2
  1. If I draw a triangle length of whose two sides are 5 cm and 4 cm and the measurement of…
Lets Work Out 21
  1. Let’s draw a triangle whose two sides are 6cm and 7cm and the measurement of the angle…
  2. Let’s construct a triangle whose length of two sides are 6cm. and 9cm. and the…
Lets Do 21.1
Question 1.

Let's draw a triangle whose two angles are of measurements 45° and 30° and length of the opposite side of 30° angle is 6 cm. Now I construct the above triangle and write down the steps of construction and prove it logically.
Answer:

Given: 1st angle = 45° and 2nd angle = 30°

and the side opposite of 30° angle is of 6cm


Steps of Construction:


Step 1:


Draw a line using the scale AB.



Step 2:


At A, draw an angle of 90° using compass and scale by standard procedure and then bisect the angle at 45°



Step 3:


Now, again take a compass keep the needle on point B and draw an angle of 30°.



Step 4:


Take distance 6cm in compass keep the needle of the compass on point A and mark an arc intersecting ray drawn in step 2. Mark the intersection point as C and join BC
Lets Do 21.2
Question 1.

If I draw a triangle length of whose two sides are 5 cm and 4 cm and the measurement of the angle opposite to the side of length 4 cm is 45°, then let's see what type of triangle I shall get. It is seen that it is not possible to draw any triangle with these conditions.
Answer:

Given: Length of two sides 5cm and 4cm

and the angle opposite to the side of length 4 cm is 45°


So, let’s start the construction step–by–step:


Step 1:


Draw the base of triangle AB = 5cm



Step 2:


At A, construct an angle ∠XAB = 90° with the help of compass and scale and then bisect the angle XAB at 45°



Step 3:


Take distance 4cm in compass keep the needle of the compass on point B and mark an arc intersecting ray drawn in step 2.



Step 4:


Mark the intersection point as C and join BC
Lets Work Out 21
Question 1.

Let’s draw a triangle whose two sides are 6cm and 7cm and the measurement of the angle opposite to the side of length 7cm. is 60°. Let’s write what will the measurement of the sides to form a triangle.
Answer:

Let the triangle be ΔABC with AB = 6 cm and BC = 7 cm


Now angle opposite to side with length 7 cm that is angle opposite to side BC is ∠A which is 60°


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 = 60° but we don’t know the length of AC so we will just draw a ray at angle 60°



Step3: As BC is 7 cm we will take 7 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



AC is 7.7 cm
Question 2.

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.
Answer:

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