Construct a triangle ABC with BC = 6 . 5 cm , &ang; B = 60 ° and &ang; C = 30 ° . Measure &ang; A .

Given: ∠ B = 60 ° , ∠ C = 30 ° , B C = 6 cm Here we need to construct the triangle △ A B C and measure the angle ∠ A . Steps :- 1) Draw the line segment B C of 6 . 5 cm . 2) Make an angle ∠ A B C = 60 ° with B as its centre by using a protractor. 3) Make an angle ∠ A C B = 30 ° with C as its centre by using a protractor. 4) The rays produced by the angles at the points B and C , intersecting at the point A . 5) Thus, we have the triangle △ A B C . Now we have the figure as follows. Now by measuring the angle by using a protractor, we get ∠ A = 90 ° .

Construct a ∆ ABC with AB = 5 cm , BC = 4 cm and CA = 3 cm . Measure &ang; ACB .

Given AB = 5 cm , BC = 4 cm and CA = 3 cm . Here we need to construct a triangle △ A B C and measure ∠ A C B . Step 1: Draw the line segment A B of 5 cm Step 2: Draw two arcs of radii 3 cm and 4 cm with centres A and B respectively, such that they are intersecting at the point C . Step 3: Join A C and B C Step 4: Now we have the triangle △ A B C Thus, we have the figure as follows By measuring the angle, we get ∠ ACB = 90 ° . Therefore, the obtained triangle is a right-angled triangle.

Construct the ∆ ABC such that BC = 6 cm , &ang; B = 45 ° and &ang; A = 75 ° .

Given that in △ A B C , B C = 6 cm , ∠ B = 45 ° , ∠ A = 75 ° . Here we need to construct a triangle by using ruler and compass. Now follow the steps to construct the triangle. 1) Draw a ray B R 2) Draw an arc of radius 6 cm with A as its centre such that it intersect B R at C . 3) Now construct ∠ C B P = 45 ° using the compass. 4) Similarly construct ∠ B C Q = 75 ° using compass such that the ray C Q intersect B P at A for the required triangle △ A B C . Hence, the required triangle is,

Construct a triangle PQR such that PQ = 6 . 3 cm , PR = 5 . 6 cm and &ang; P = 48 ° .

Given , P Q = 6 . 3 cm , P R = 5 . 6 cm and ∠ P = 48 ° Steps 1 ] Draw the ray P X 2 ] Draw an arc of an radius 6 . 3 cm ( = P Q ) at center P to intersect P X at point Q 3 ] Make the angle ∠ Q P Y = 48 ° by using the protractor . 4 ] Draw an arc of an radius 5 . 6 cm with P a s its centre such that it intersect P Y at the point R 5 ] Join the line R Q for the required triangle .

E M B I B E

Essential ICSE Mathematics for Class 6>Geometry>Chapter 18 - Triangles>EXERCISE 4B

Asit Das Gupta and Alok Kumar Solutions for Exercise 2: EXERCISE 4B

Author:Asit Das Gupta & Alok Kumar

Asit Das Gupta Mathematics Solutions for Exercise - Asit Das Gupta and Alok Kumar Solutions for Exercise 2: EXERCISE 4B

Attempt the free practice questions from Exercise 2: EXERCISE 4B with hints and solutions to strengthen your understanding. Essential ICSE Mathematics for Class 6 solutions are prepared by Experienced Embibe Experts.