Page 1 :
MCO WORKSHEET-1, CLASS X: CHAPTER — 9, SOME APPLICATIONS TO TRIGONOMETRY,, , 1. The angle of elevation of the top of a tower from a point on the ground, which is 20m away from, the foot of the tower is 60", Find the height of the tower., , (a) 10.43 m (b) 30/3 m (c)20.V3 m_— (d) none of these, , , , 2. The height of a tower is 10m. What is the length of its shadow when Sun's altitude is 45°?, (a) 10m (b) 30 m (c) 20m (d) none of these, , 3. The angle of elevation of a ladder leaning against a wall is 60" and the foot of the ladder is 9.5 m, away from the wall. Find the length of the ladder., (a) LOm (b) 19m (c) 20m (d) none of these, , 4. If the ratio of the height of a tower and the length of its shadow is V3 51, what is the angle of, elevation of the Sun?, (a) 30° (b) 60” (c) 45" (d) none of these, , 5. What is the angle of elevation of the Sun when the length of the shadow of a vertical pole is, equal to its height?, (a) 30° (b) 60° (©) 45° (d) none of these, , 6. From a point on the ground, 20 m away from the foot of a vertical tower, the angle of elevation, of the top of the tower is 60", what is the height of the tower?, , (a) 103 m (b) 30V3 m (c) 20V3 m_ (d) none of these, 7. If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from, the base of the tower and in the same straight line with it are complementary, find the height of, , the tower,, (a) 10m (b)6m (c)8m (d) none of these, , 8. In the below fig. what are the angles of depression from the observing positions D and E of the, object A?, (a) 30°, 45° (b) 60”, 45° (c) 45", 60" (d) none of these, of, , Le, , , , c B A, , 9. The ratio of the length of a rod and its shadow is 1: V3. The angle of elevation of the sun is, (a) 30° (b) 60” (c) 45° (d) none of these, , 10. If the angle of elevation of a tower from a distance of 100m from its foot is 60", then the height, of the tower is, , (a) 100¥3 m —(b) 5 m ()50V3 md) * m
Page 2 :
§, , %, , MCO WORKSHEET-II, CLASS X; CHAPTER — 9, SOME APPLICATIONS TO TRIGONOMETRY, , If the altitude of the sun is at 60°, then the height of the vertical tower that will cast a shadow of, length 30m is, , (a) 30¥3 m (b) 15 m (c) 5 m= (d) 15J2 m, , , , A tower subtends an angle of 30” at a point on the same level as its foot. At a second point ‘h’, metres above the first, the depression of the foot of the tower is 60", The height of the tower is, , h h h, — b) + ©) V3h d, (5m (b) =m (c) hm @ am, , A tower is 100¥3 m high. Find the angle of elevation if its top from a point 100 m away from its, foot., (a) 30° (b) 60° (c) 45° (d) none of these, , The angle of elevation of the top of a tower from a point on the ground, which is 30m away from, the foot of the tower is 30°, Find the height of the tower., , (a) 10V3 m (b) 303 m (c)20,¥3 m_ (d) none of these, , The string of a kite is 100m long and it makes an angle of 60” with the horizontal, Find the, height of the kite, assuming that there is no slack in the string., , (a) 100J3 m (by as m (c) 503 m (a) * m, , A kite is flying at a height of 60m above the ground. The inclination of the string with the ground, is 60". Find the length of the string, assuming that there is no slack in the string., , (a) 40/3 m (b) 30,3 m (c) 20-43 m_ (d) none of these, , A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a, vertical pole to the ground, Find the height of the pole if the angle made by the rope with the, ground level is 30"., , (a) 10m (b) 30 m (c) 20m (d) none of these, , A tower is 50m high, Its shadow ix ‘x’ metres shorter when the sun’s altitude is 45° than when it, is 30", Find the value of ‘x’, , (a) 100. J3 m (b) * m (c) 50.43 m_ (d) none of these, , Find the angular elevation of the sun when the shadow of a 10m long pole is 10¥3 m., (a) 30" (b) 60° (c) 45° (d) none of these, , 10. A vertical pole stands on the level ground. From a point on the ground 25m away from the foot, , of the pole, the angle of elevation of its top is found to be 60", Find the height of the pole., (a) 253 m (b) 5 m (c) 50-43 m_ (d) none of these
Page 3 :
MCO WORKSHEET-II|, CLASS X: CHAPTER — 9, SOME APPLICATIONS TO TRIGONOMETRY, , 1. A kite is flying at a height of 75m above the ground. The inclination of the string with the ground, is 60", Find the length of the string, assuming that there is no slack in the string., (a) 40/3 m (b) 30V3 m (c) 50V3 m_ (d) none of these, , 2. The angle of elevation of the tope of a tree from a point A on the ground is 60°, On walking 20m, away from its base, to a point B, the angle of elevation changes to 30°. Find the height of the, tree., , (a) 10V3 m ——(b) 30V3 m (c) 203 m_(d) none of these, , 3. A 1.5m tall boy stands at a distance of 2m from lamp post and casts a shadow of 4.5m on the, ground, Find the height of the lamp post., (a) 3m (b) 2.5 m (c)Sm (d) none of these, , 4. The height of the tower is 100m, When the angle of elevation of the sun changes from 30” to 45°,, the shadow of the tower becomes ‘x’ meters less. The value of *x’ is, , (a) 10043 m — (b) 100m (c) 100.43 1) m wr, , 5. The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an, angle of 30° with horizontal, then the length of the wire is, (a) 12m (b) 10m (c)8m (d) 6m, , 6. If the angles of elevation of a tower from two points distant a and b (a > b) from its foot and in, the same straight line from it are 30” and 60°, then the height of the tower is, , (a) Va+b m (b) va—b m (c) Jab m (d) & m, , 7. The angles of elevation of the top of a tower from two points at a distance of ‘a’ mand ‘b’ m, from the base of the tower and in the same straight line with it are complementary, then the, height of the tower is, , (a) Ja+b m (b) Ja=b m (c) Jab m () fi m, , 8. From the top of a cliff 25m high the angle of elevation of a tower is found to be equal to the, angle of depression of the foot of the tower, The height of the tower is, (a) 25 m (b) 50m (c) 75m (d) 100m, , 9. If the angle of elevation of a cloud from a point 200m above a lake is 30° and the angle of, depression of its reflection in the lake is 60°, then the height of the cloud above the lake is, (a) 200 m (b) 500 m (c) 30m (d) 400 m, , 10. The angle of elevation of a cloud from a point *h’ meter above a lake is ‘ct’, The angle of, depression of its reflection in the lake is 45”, The height of the cloud is, A(L+ tana) ACL—tan a), , (a) b.tanc (b) —————— Oo-—— (d) none of these, (l=tana) (i+tana)
Page 4 :
MCO WORKSHEET-I, CLASS X: CHAPTER —10, CIRCLES, , 1, Find the length of tangent drawn to a circle with radius 7 cm from a point 25 cm away from the, centre,, (a) 24 em (b) 27 cm (c) 26 cm (d) 25 cm, , 2. A point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to, the circle is 24 cm, Find the radius of the circle., (a) Lem (b) 10cm (c) 16cm (d) 1S em, , 3. From an external point P, tangents PA und PB are drawn to a circle with centre O, If CD is the, tangent to the circle at a point E and PA = 14 cm, find the perimeter of the APCD,, (a) 28 cm (b) 27 cm (c) 26cm (d) 25 cm, , “Ce, , 4. In the above sided figure, PA and PB are tangents such that PA = = Sem and ZAPB = 60). Find the, length of the chord AB., (a) 4m (b) Tem (c)6cm (d) 9 em, , , , 5. In the below figure the circle touches all the sides of a quadrilateral ABCD whose three sides are, AB = 6 cm, BC = 7 cm, CD = 4 cm, Find AD,, (a) 4m (b) 3 cm (c) 6cm (d) 9 om, , Cc T, XY) 3, A, B, , 6, In the above sided Fig,, if TP and TQ are the two tangents to a circle with centre O so that, ZPOQ = 110°, then ZPTQ is equal to, (a) 60° (b) 70° (c) 80° (d) 90”, , 7, If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle, of 80°, then 2POA is equal to, (a) 60° (b) 70° (c) 80° (d) 50°
Page 5 :
MCQ WORKSHEET-II, , CLASS X: CHAPTER — 10, CIRCLES, , 1, In below Fig, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If 4 DBC =, 55° and ZBAC = 45°, find ZBCD., {a) 80° (b) 60" {c) 90" (d) none of these, , D B c, Ka/, A <b, B Cc a, , 2. In above sided Fig, A,B and C are three points on a circle with centre O such that ZBOC = 30°, and ZAOB = 60°, If D is a point on the circle other than the are ABC, find ZADC,, (a) 45° (b) 60" (c) 90" (d) none of these, , , , 3. A chord of a circle is equal to the radius of the circle, Find the angle subtended by the chord at a, , point on the minor arc, (a) 150° (b) 30° (c) 60" (d) none of these, , 4. A chord of a circle is equal to the radius of the circle, Find the angle subtended by the chord at a, point on the major arc., (a) 150" (b) 30° (c) 60" (d) none of these, , 5. In the below Fig., ZABC = 69°, ZACB = 31°, find ZBDC., (a) 80" (b) 60" (c) 90° (d) 100", D, , , , 6. In the above sided Fig,, A, B, C and D are four points on a circle, AC and BD intersect at a point, , E such that ZBEC = 130° and ZECD = 20°. Find ZBAC., (a) 110" (b) 150° (c) 90° (d) 100", , 7. ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ZDBC = 70°, ZBAC is, 30°, find ZBCD., (a) 80° (b) 60" (c) 90° (d) 100"
