ASSIGNMENT CLASS X APPLICATIONS OF TRIGONOMETRY

1. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 10 m. Find the height of the tree before it was broken.

2. From the top of a building 60 m high the angles of depressions of the top and the bottom of a tower are observed to be 30° and 60°. Find the height of the tower.

3. From a point on the ground the angles of elevation of the bottom and top of a water tank kept at the top of 20 m high tower are 45° and 60°. Find the height of the water tank.

4. A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 meters away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the width of the river.

5. The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°.Find the height of the tower and the distance of the tower from the point A.

6. A flagstaff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flag-staff is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the flag-staff.

7. The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10 m longer than when it was 60°. Find the height of the tower.

8. On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.

9. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30°. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45°. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl.

10. From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30°.From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°.Find the height of the tower and the distance between the tower and the building.

11.At a point on the level ground the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 m towards the tower, the tangent of the angle is found to be3/4 . Find the height of the tower.

12. Two men on either side of a cliff 80 m high observe the angles of elevation of top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

13. An aeroplane, when 1500 m high passes vertically above another aeroplane at an instance when the angles of the two aeroplanes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the two aeroplanes.

14. The angles of elevation of the top of a tower from two points on the ground at distances 9m and 4m from the base of the tower are in same straight line with it are complementary. Find height of the tower.

15. The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 60 m, find the height of the first tower.

APPLICATION OF TRIGONOMETRY(Height and Distance) 10th maths test paper

Math Adda 

Q1 A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60°with the wall, find the height of the wall.                                                                                  (7.5 √3 )

Q 2  A pole 12 m high casts a shadow 4 √3 m long on the ground. Find the angle of elevation        (60°)

Q 3 The angle of elevation of the top of a tower from a point on the ground is 30° if on walking 30m towards the tower, the angle of elevation becomes 60°.Find the height of the tower.(15√3 )

Q 4 An observer 1.5m tall is 20.5m away from a tower 22m high. Determine the angle of elevation of the top of the tower from the eye of the observer.                                       (45°)

Q 5 An aero plane when flying at a height of 5000m from the ground passes vertically above another aero plane at an instant when the angles of the elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aero planes at the instant.                                                                                           (2116.5m)

CBSE TEST PAPER Chap-4(co-ordinate geometry)

Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2       (B) 3         (C) 1                           (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                            (B) 8                (C) 4                           (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8                            (B) 2 √7          (C) 10                         (D) 6

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5                           (B) 5√ 2          (C) 2 √5                      (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                            (B) 3                (C) √ 34                   (D) 4  

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the 
ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7) is equal, show that 3x = 2y.

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by  [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that   x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q.

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability