# Trigonometry Part 4: Advance math series 2000 most important questions.

## Trigonometry Part 4: Advance math series 2000 most important questions.

Trigonometry Part 4: Advance math series 2000 most important questions.

Q121. If θ is an acute angle and tanθ = 1 then

(a)

(b) some price number of pn for p and some for n ≥2

(c) some different prime number of p1, p2 for p1&p2

(d)

Q122.

(a) – 2/√3

(b) √3

(c) – √3

(d) 3

Q123. If   then the value of

(a) a

(b) 2a

(c) 3a

(d) 4a

Q124.  is equals to

(a) 1

(b) 2

(c) 3

(d) 4

Q125. If the angle of elevation of the Sun changes from 30° to 45º, the length of the shadow of a pillar decreases by 20 metres.The height of the pillar is

(a)20(√3-1) m

(b) 20(√3+1) m

(c) 10(√3-1) m

(d) 10(√3+1) m

Q126. One flies a kite with a thread 150 metre long. If the thread of the kite makes an angle of 60° with the horizontal line, then the height of the kite from the ground (assuming the thread to be in a straight line) is

(a)50 metre

(b) 75√3 metre

(c) 25√3 metre

(d) 80 metre

Q127. The angle of elevation of the top of a tower from two points A and B lying on the horizontal through the foot of the tower are respectively 15° and 30°.  If A and B are on the same side of the tower and AB = 48 metre, the height of the tower is:

(a)24√3 metre

(b) 24 metre

(c) 24√2 metre

(d) 96 metre

Q128. At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 1/5, on walking 138 metres towards the monument the secant of the angle of elevation is found to be . The height of the monument (in metre) is

(a)35

(b) 49

(c) 42

(d) 56

Q129. The distance between two pillars of length 16 metres and 9 metres is x metres.  It two angles of elevation of their respective top from the bottom of the other are complementary  to each other, then the value of x(in metres) is

(a)15

(b) 16

(c) 12

(d) 9

Q130. The angle of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then (in metre) the height of the building is

(a)

(b)

(c)

(d)

Q131. 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°. The height of the tower is

(a)√3 m

(b) 5√3  m

(c) 10√3  m

(d) 20√3  m

Q132. Two poles of equal height are standing opposite to each other on either side of a road which is 100m wide. From a point between them on road, angle of elevation of their tops are 30° and 60°. The height of each pole (in metre) is

(a)25√3

(b) 20√3

(c) 28√3

(d) 30√3

Q133. A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of 8√3 metres from its foot and makes an angle of 30°, then the height of the post is:

(a)16 metres

(b) 23 metres

(c) 24 metres

(d) 10 metres

Q134. The angle of elevation of the top of a building and the top of the chimney on the roof of the building from a point on the ground are x and 45° respectively.  The height of building is h metre. Then the height of the chimney, (in metre) is:

(a)h cot x + h

(b) h cot x – h

(c) h tan x – h

(d) h tan x + h

Q135. Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is

(a) x/2√2

(b) x/4

(c) x√2

(d) x/√2

Q136. An aeroplane when flying at a height of 5000 m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same points on the ground are 60° and 45° respectively.  The vertical distance between the aeroplanesat that instant is

(a)5000(√3- 1) m

(b) 5000(3 -√3) m

(c) 5000(1-1/√3) m

(d) 4500 m

Q137. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance towards the tower and then his angle of elevation of the top of the tower is 60°. If the height of the tower is 30 m, then the distance he moves is

(a)22 m

(b) 22√3 m

(c) 20 m

(d) 20√3 m

Q138. The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angle of elevation of the top of the poles from the middle point of the line segment  joining  their feet are complementary to each other. The height of the poles are:

(a)10 m and 20 m

(b) 20 m and 40 m

(c) 20.9 m and 41.8 m

(d) 15√2 m and 30√2  m

Q139. An aeroplane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 30° and 60° respectively.  The distance between the two planes at that instant is

(a)6520 m

(b) 6000 m

(c) 5000 m

(d) 6250 m

Q140. The shadow of the tower becomes 60 metres longer when the altitude of the sun changes from 45°  to 30°. Then the height of the tower is

(a)20 (√3+1) m

(b) 24 (√3+1) m

(c) 30 (√3+1) m

(d) 30 (√3-1) m

Q141. A vertical post 15 ft high is broken at a certain height and its upper part, not completely separated, meets the ground at an angle of 30°. Find the height at which the post is broken.

(a)10 ft

(b) 5 ft

(c) 15√3(2-√3) ft

(d) 5 √3 ft

Q142. The shadow of a tower is √3 times it height. Then the angle of elevation of the top of the tower is

(a) 45°

(b) 30°

(c) 60°

(d) 90°

Q143. A man 6 ft tall casts a shadow 4 ft long, at the same time when a flag pole casts a shadow 50 ft long.  The height of the flag pole is

(a)80 ft

(b) 75 ft

(c) 60 ft

(d) 70 ft

Q144. The angle of elevation of an aeroplane from a point on the ground is 60°. After 15 seconds flight, the elevation changes to flight, the elevation changes to 30°. If the aeroplane is flying at a height of 1500√3 m, find the speed of the plane

(a)300m/sec

(b) 200m/sec

(c) 100m/sec

(d) 150m/sec

Q145. The angle of elevation of the top of a tower from the point P and Q at distance of ‘a’ and ‘b’ respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is

(a) √ab

(b) a/b

(c) a b

(d) a2 b2

Q146. The angle of elevation of a tower from a distance 100 m from its foot is 30°. Height of the tower is:

(a) 100/√3 m

(b) 50√3 m

(c) 200/√3 m

(d) 100√3 m

Q147. A pole stands vertically, inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ΔABC, the foot of the pole is at the

(a)centroid

(b) circumcentre

(c) incentre

(d) orthocenter

Q148. If the angle of elevation of a balloon from two consecutive kilometre – stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be

(a)√3/2 km

(b)1/2  km

(c) 2/√3km

(d) 3√3 km

Q149. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is

(a)72 m

(b) 60 m

(c) 65 m

(d) 70 m

Q150. A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before.  The height of the tower is

(a)80 m

(b) 100 m

(c) 160 m

(d) 200 m

Q151. The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is

(a)50√3 m

(b)  50/√3 m

(c) 75 √3 m

(d)  75/√3 m

Q152. The length of the shadow of a vertical tower on level ground increases by 10 metres when the altitude of the sun changes from 45to 30. Then the height of the tower is

(a)5√3 metre

(b) 10(√3+1) metre

(c) 5(√3+1) metre

(d) 10√3 metre

Q153. The elevation of the top of a tower from a point on the ground is 45°.  On travelling 60 m from the point  towards the tower.  The  elevation of the top becomes 60°. The height of the tower (in metres) is

(a)30

(b) 30(3 -√3 )

(c) 30(3 +√3 )

(d) 30√3

Q154. From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other.  If the distance of the two points from the foot of the pillar are9 metres and 16 metres and the two points lie on the same side of the pillar, then the height of the pillar is

(a)5 m

(b) 10 m

(c) 7 m

(d) 12 m

Q155. From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°.  Find the length of the flagstaff. (Take √3 = 1.732)

(a)10( √3+ 2) m

(b) 10( √3+ 1) m

(c) 10√3 m

(d) 7.32 m

Q156. The angle of elevation of the top of a vertical tower situated per perpendicularly on a plane is observed as 60° from a point P on the same plane. From another point Q. 10m vertically above the point P, the angle of depression of the foot of the tower is 30°. The height of the tower is

(a)15 m

(b) 30 m

(c) 20 m

(d) 25 m

Q157. From a point 20 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. The height of the tower is

(a)10√3 m

(b) 20√3  m

(c) 10/√3 m

(d) 20/√3 m

Q158. The angle of elevation of a ladder leaning against a house is 60° and the foot of the ladder is 6.5 metres from the house. The length of the ladder is

(a)13/√3 metres

(b) 13 metres

(c) 15 metres

(d) 3.25 metres

Q159. The angle of elevation of sun changes from 30° to 45° , the length of the shadow of a pole decreases by 4 metres, the height of the pole is (Assume √3 = 1.732)

(a)1.464 m

(b) 9.464 m

(c) 3.648 m

(d) 5.464 m

Q160. A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depression of the foot of the tower are 60 and 30 respectively.  The height of the tower is

(a)20 m

(b) 30 m

(c) 40 m

(d) 50 m