Chapter 8 Introduction to Trigonometry Ex 8.2
Chapter 8 Introduction to Trigonometry Ex 8.2 Question 1. Evaluate the following: Solution: Question 2. Choose the correct option and justify your choice: Solution: Question 3. Question 4. State whether the following statements are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B. (ii) The value of […]
Chapter 8 Introduction to Trigonometry Ex 8.1
Chapter 8 Introduction to Trigonometry Ex 8.1 Question 1. In ∆ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C Solution: Question 2. In given figure, find tan P – cot R. Solution: Question 3. Question 4. Given 15 cot A […]
Chapter 7 Coordinate Geometry Ex 7.4
Chapter 7 Coordinate Geometry Ex 7.4 Question 1. Determine the ratio, in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, -2) and B(3, 7). Solution: Question 2. Find a relation between x and y, if the points (x, y), (1, 2) and (7, 0) are […]
Chapter 7 Coordinate Geometry Ex 7.3
Chapter 7 Coordinate Geometry Ex 7.3 Question 1. Find the area of the triangle whose vertices are: (i) (2, 3), (-1, 0), (2, -4) (ii) (-5, -1), (3, -5), (5, 2) Solution: Question 2. In each of the following find the value of ‘k’ for which the points are collinear. (i) (7, -2), (5, 1), […]
Chapter 7 Coordinate Geometry Ex 7.2
Chapter 7 Coordinate Geometry Ex 7.2 Question 1. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3. Solution: Question 2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3). Solution: Question 3. Solution: […]
Chapter 7 Coordinate Geometry Ex 7.1
Chapter 7 Coordinate Geometry Ex 7.1 Question 1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b) Solution: Question 2. Find the distance between the points (0, 0) and (36, 15). Solution: Let points be A (0, 0) and B […]
Chapter 6 Triangles Ex 6.6
Chapter 6 Triangles Ex 6.6 Question 1. Solution: Question 2.In the given figure, D is a point on hypotenuse AC of ∆ABC, DM ⊥ BC and DN ⊥ AB. Prove that:(i) DM2 = DN X MC (ii) DN2 = DM X AN Solution: Question 3.In the given figure, ABc is triangle in which ∠ABC > 90° and AD ⊥ CB […]
Chapter 6 Triangles Ex 6.5
Chapter 6 Triangles Ex 6.5 Question 1. Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 […]
Chapter 6 Triangles Ex 6.4
Chapter 6 Triangles Ex 6.4 Question 1. Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC. Solution: Since, ∆ABC ~ ∆DEF The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides. Question 2. […]
Chapter 6 Triangles Ex 6.3
Chapter 6 Triangles Ex 6.3 Question 1. State which pairs of triangles in the given figures are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form : Solution: Question 2. In the given figure, ∆ODC ~ ∆OBA, ∠BOC = 125° […]