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Trigonometry Part 5: Advance math questions.

Trigonometry Part 5: Advance math questions.

Q161. The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from 45° to 30°. Then the height of the tower is

(a)5( √3+ 1) metres

(b) 5( √3- 1) metres

(c) 5 √3 metres

(d) 5/√3 metres

Q162. If a pole of 12 m height casts a shadow of 4√3 m long on the ground, then the sun’s angle of elevation at that instant is

(a) 30°

(b) 60°

(c) 45°

(d) 90°

Q163. The angle of elevation of the top of a tower from a point on the ground is 30° and moving 70 metres towards the tower it becomes 60°. The height of the tower is

(a)10 metre

(b)10/√3  metre

(c) 10√3 metre

(d) 35√3 metre

Q164. In circular measure, the value of the angle 11°15’ is

(a) π°/16

(b) π°/8

(c) π°/4

(d) π°/12

Q165. In a triangle ABC, ΔABC = 75° and ΔABC =π°/4. The circular measure of ΔBAC is Q166. The circular measure of an angle of an isosceles triangle is 5π/9. Circular measure of one of the other angles must be

(a) 5π/8

(b) 5π/9

(c) 2π/9

(d) 4π/9

Q167. The degree measure of 1 radian (taking π = 22/7) is

(a)57°61’22” (approx.)

(b) 57°16’22” (approx.)

(c) 57°22’16” (approx.)

(d) 57°32’16” (approx.)

Q168. 3π/5 radians is equal to

(a)100°

(b) 120°

(c) 108°

(d) 180°

Q169. If the sum of two angles is 135° And their difference is π/12 , then the circular measure of the greater angle is

(a) 2π/3

(b) 3π/5

(c) 5π/12

(d) π/3

Q170. There are two vertical posts, one on each side of a road. Just opposite to each other. One post is 108 metre high. From the top of this post, the angle of depression of the top and foot of the other post are 30° and 60° respectively. The height of the other post (in metre) is

(a) 36

(b) 72

(c) 108

(d) 110

Q171. There are two temples, one on each bank of a river, just opposite to each other. One temple is 54 m high.  From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. The length of the temple is:

(a) 18 m

(b) 36 m

(c) 36√3 m

(d) 18√3 m

Q172. The top of two poles of height 24 m are 36m are connected by a wire. If the wire makes an angle of 60° with the horizontal. Then the length of the wire is

(a) 6 m

(b) 8√3 m

(c) 8 m

(d) 6√3 m

Q173. From the top of a hill 200 m high, the angle of depression of the top and the bottom  of a tower are observed to be 30° and 60°. The height of the tower is (in m):

(a) 400√3/3

(b) 166 (c) 133 (d) 200√3

Q174. From a tower 125 metres high, the angle of depression of two objects, which are in horizontal line through  the base of the tower, are 45° and 30° and they are on the same side of the tower. The distance (in metres) between the objects is

(a) 125√3

(b) 125(√3- 1)

(c) 125/(√3 – 1)

(d) 125( √3+ 1)

Q175. From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 30° and 45°. Then the distance between the objects are

(a) 180 (3 +√3) m

(b) 180 (3 -√3) m

(c) 180 ( √3– 1) m

(d) 180 ( √3+ 1) m

Q176. From the peak of a hill which is 300 m high, the angle of depression of two sides of a bridge lying on a ground are 45° and 30° (both ends of the bridge are on the same side of the hill). Then the length of the bridge is

(a) 300 ( √3– 1) m

(b) 300 ( √3+ 1) m

(c) 300√3 m

(d) 300/√3 m

Q177. From an aeroplane just over a river, the angle of depression of two palm trees on the opposite bank of the river are found to be 60° and 30° respectively. If the breadth of the river is 400 metres, then the height of the aeroplane above the river at that instant is

(Assume  √3 = 1.732)

(a) 173.2 metres

(b) 346.4 metres

(c) 519.6 metres

(d) 692.8 metres

Q178. If tan θ = 1, then the value of (a) 2

(b) 2 (c) 3

(d) 4/5

Q179. If θ is a positive acute angle and cos2θ + cos4 θ = 1 then the value of tan2 θ + tan4 θ is

(a) 3/2

(b) 1

(c) ½

(d) 0

Q180. What is the value of tan 4°.tan 43°.tan 47°.tan 86° ?

(a) 0

(b) 1

(c) √3

(d) 1/√3

Q181. If then the value of is

(a) 0.5

(b) – 0.5

(c) 3.0

(d) -3.0

Q182. If tan 15°=2-√3 then tan 15° cot75°+ tan75° cot15° is

(a) 14

(b) 12

(c) 10

(d) 8

Q183. If θ is an acute angle and tanθ+cotθ=2 then tan 5 θ cot 10 θ is

(a) 1

(b) 2

(c) 3

(d) 4

Q184. What will be the value of (sin21°+sin23°+sin25°+……………..+sin285°+sin287°+sin289°)?

(a) 21 (b) 22

(c) 22 (d) 23 Q185. If sin θ – cos θ = 7/13 and 0< θ < 90° then what is the value of  sin θ + cos θ ?

(a) 17/13

(b) 13/17

(c) 1/13

(d) 1/17

Q186. If sinα + cosβ =2 (0° ≤ a ≤ 90°) then what will be the value of sin (a) sin a/2

(b) cos a/3

(c) sin a/3

(d) cos 2a/3

Q187. If cosθ – sinθ then what will be the value of 2 cos2 θ -1

(a) 0

(b) 1

(c) 2/3

(d) 3/2

Q188. What is the value of cot 10° . cot 20° . cot 60° . cot 70° . cot 80°.

(a) 1

(b) – 1

(c) √3

(d) 1/√3

Q189. If sin a sec ( 30° + a ) = 1 (0< a < 60° ), the value of sin a + cos 2a is

(a) 1

(b) (c) 0

(d) √2

Q190. What will be simplified value of (secA – cosA)2 + (cosec A- sinA)2 – (cot A – tanA)2 ?

(a) 0

(b) 1/2

(c) 1

(d) 2

Q191. If θ is an acute angle and 7 sin2 θ+ 3cos2θ then what is the value of tan θ ?

(a) √3

(b) 1/√3

(c) 1

(d) 0

Q192. What is the value of sin2 1°+ sin2 5° + sin2 9° + …….. + sin2 89° ?

(a) 11 (b) 11 √2

(c) 11

(d) 11/ √2

Q193.  The numerical value of cot 18°(cot 72° cos2 22° + ) is

(a) 1

(b) √2

(c) 3

(d) 1/√3

Q194. If A = sinθ + cos2 θ  for any value of  then what is the value of A ?

(a) (b) (c) (d) Q195. If sinθ + cosecθ = 2, then in the situation of 0° ≤ θ ≤ 90°. What will be the value of sin5 θ + cosec5 θ ?

(a) 0

(b) 1

(c) 10

(d) 2

Q196. sin2 5° sin210° + sin2 15°+ ………. + sin2 85° + sin2 90° will be equal to

(a) 7 (b) 8 (c) 9

(d) 9 Q197. If tan 2θ.tan4θ =1, then the value of tan3θ is

(a) √3

(b) 0

(c) 1

(d) 1/√3

Q198. If 2 cosθ – sinθ = 1/ √2 , (0° < θ < 90°) then the value of 2 sin θ + cos θ is

(a) 1/√2

(b) √2

(c)  3/√2

(d) √2/3

Q199. If then the value of sin4 θ – cos4 θ is

(a) 1/5

(b) 2/5

(c) 3/5

(d) 4/5 Q200. The value of tan1°.tan2°.tan3°.tan4°………………tan87°.tan88°.tan89° is

(a) 1/√3

(b) √3

(c) 1

(d) Not defined

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