# HEIGHT and DISTANCE – TRIGONOMETRY Quantitative Aptitude

Height and Distance is one the important part of Trigonometry segment in Quantitative Aptitude or Arithmetic Aptitude. Upjob.in now publishing the fully solved Question paper, Problem and Numerical with answer key for the preparation of banking examination. Today we are covering the important topic of Math for SSC, bank, and railway test. Hope following MCQ will be helpful in the preparation of your Banking examination.
Q1. If triangle ABC is right angled at B, then which of the following true?
(a) AB/AC= sin C     (b) BC/AB= tan C       (c) AC/AB= cos C    (d) AB/BC= sec C
Ans. (a)

Q2. If tan x = 3/4 and x is acute, then cosec x=?
(a) 5/4    (b) 5/3      (c) 4/3      (d) 4/5
Ans. (b)

Q3. If 5 tan x= 4, then (5sinx- 3 cos x/ 5 sin x +3 cos x) =?
(a )2/5    (b) 1/7      (c) 2/7     (d) 5/7
Ans. (b)

Q4. If 3 cot x= 4, then (5sin x +3 cos x/ 5 sin x - 3 cos x) =?
(a) 1/9    (b) 1/3      (c) 3     (d) 9
Ans. (d)

Q5. If sin A: cos A= 4:7, then (7sin A-3cosA/ 7sinA + 2cosA) =?
(a) 1/6    (b) 1/3     (c) 3/14     (d) 3/2
Ans. (a)

Q6. If (tan x +cot x) =5, then (tan square x + cot square x) =?
(a) 25    (b) 27      (c) 23    (d) 24
Ans. (c)

Q7. sin 60 cos 30+ cos 60 sin 30=?
(a)  3/2    (b) 5/2      (c) 1    (d) 2
Ans. (c)

Q8. sin square 60+ cos square 30 + cot square 45 + sec square 60 –cosec square 30= ?
(a) 5/2    (b) 3/2      (c) 7/2    (d) 1/2
Ans. (a)

Q9. (2sin square 30- 3cos square 45+ tan square 60) =?
(a) 1    (b) 2      (c) 5    (d) 4
Ans. (a)

Q10. If x tan 45 cos 60= sin 60 cot 60, then find the value of x
(a) 2   (b) 7      (c) 3    (d) 1
Ans. (d)

Q11. sin 19/cos 71+ cos 73/sin 17=?
(a) 0    (b) 1/2      (c) 1    (d) 2
Ans. (d)

Q12. sin square 25 + sin square 65=?
(a) 1    (b) 0      (c) 2 cos square 65    (d) 2 sin square 65
Ans. (a)

Q12. cos square 75 + cos square 15=?
(a) 1    (b) 0      (c) 2 cos square 65    (d) 2 sin square 65
Ans. (a)

Q13. sin 20 cos 70 + cos 20 sin 70=?
(a) 0    (b) 1     (c) 2    (d) None of these
Ans. (b)

Q14. cos 64 cos 26 – sin 64 sin 26=?
(a) 0    (b) 1      (c) 2 cos 64    (d) 2 sin 26
Ans. (a)

Q15. sin 53 cos 37 + cos 53 sin 37=?
(a) 0    (b) 3/2      (c) 1    (d) 2
Ans. (c)

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• Q16. cos 72- sin 18 =?
(a) 0    (b) 1         (c) 2 sin 18     (d) None of these
Ans. (a)

Q17.tan 35 tan 40 tan 45 tan 50 tan 55 =?
(a) 0    (b) 1      (c) 2   (d) None of these
Ans. (b)

Q18. cos 0 =?
(a) 0    (b) 1      (c) Not defined     (d) None of these
Ans. (b)

Q19. If cos y =5/13, 0 < y < 90, then find the value of cos y + 5 cot y /cosec y-cos y =?
(a) 155/109    (b) 169/109     (c) 395/109    (d) 385/109
Ans. (d)

Q20. [(sin x/1+cos x) + (1+cos x/sin x)] =?
(a) 2    (b) 2/sin x      (c) 4/sinx cosx    (d) none of these
Ans. (b)

Q21. If sin 42 =X, then cos 48=?
(a) -X    (b) X      (c) 1 +X    (d) 1/X
Ans. (b)

Q22. sin A + sin B /cos A- cos B + cos A +cos B / sin A- sin B =?
(a) 0    (b) sin A cos B      (c) cos A cos B    (d) tan A tan B
Ans. (a)

(a) 54 degree (b) 81 degree (c) 100 degree (d) 108 degrees
Ans. (d)

Q24.  The maximum value of (sin x + cos x) is:
(a) 0    (b) 1/2      (c) 1    (d) root 2
Ans. (d)

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• Q25. [(1+ sin z/cos z) + (cos z /1 +cos z)]=?
(a) sec z    (b) 2 sec z      (c) 1/2 cos z    (d) 2 cos z
FAns. (b)

HEIGHT and DISTANCE

Q1. If a vertical pole 6 m high has a shadow of length 2
Root 3m fined the angle of elevation of the sun.
(a) 54 degree (b) 60 degree (c) 100 degree (d) 108 degrees
Ans. (b)

Q2. The angle of elevation of a tower from a distance 50m, from its foot is 30 degree. The height of the tower is
(a) 50 root 3m (b) 50/ root 3m (c) 25 root 3m (d) 100 root 3m
Ans. (b)

Q3. A 10m long ladder is placed against a wall. It is inclined at an angle of 30 degree to the ground. The distance of the foot of the ladder from the wall is
(a) 7.32m (b) 8.26m (c) 8.66m (d) 8.16m
Ans. (c)

Q4. A kite is flying at a height of 75 m from the level ground, attach to a string inclined at 60 degree to the horizontal. The length of the string is:
(a) 50/ root 3m (b) 50 root 3m (c) 25 root 3m (d) 100 root 3m
Ans. (b)

Q5. From the top of a cliff 50m high, the angles of depression of the top and bottom of a tower are observed to be 30 degree and 60 degree respectively. What is the height of the tower?
(a) 30 m (b) 45 m (c) 60 m (d) 75 m
Ans. (c)

Q6. The angles of depression of two ships from the top of the light house are 45 and 30 degree towards east. If the ships are 200 m apart, the height of the light house is: (take root 3= 1.73)
(a) 100 m (b) 173 m (c) 200 m (d) 273 m
Ans. (d)

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• Q7. The height of a tree is 10 m. It is bend by the wind in such a way that its top touches the ground and makes an angle of 60 degree with the ground. At what height from the bottom did the tree get bent? (Take root 3= 1.732)
(a) 4.6 m (b) 4.8 m (c) 5.2 m (d) 5.4 m
Ans. (a)

Q8. From a point on a bridge across the river, the angles of depression of the bank on opposite sides of the river are 30 and 45 degree respectively. If the bridge is at a height of 2.5 m from the banks, find the width of the river. (Take root 3= 1.732)
(a) 5.78 m (b) 6.83 m (c) 7.24 m (d) 6.7 m
Ans. (b)

Q9. On the horizontal plane, there is a vertical tower with a flagpole on its top. At a point 9 m away from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60 and 30 degree respectively. The height of the flagpole is:
(a) 6 root 3m                  (b) 5 root 3m                (c) 25 m                               (d) 4 m
Ans. (a)

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TIME AND WORK
Q1. A and B can do a piece of work in 8 hours while B alone can do it in 12 hours. Both A and B working together can finish the work in:
(a) 10 hours       (b) 4 hours      (c) 5 1/4 hours         (d) 4 4/5 hours

Q2. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
(a) 30 days      (b) 35 days     (c) 40 days         (d) 45 days

Q3. Kamal can do a work in 15 days. Bimal is 50 % more efficient than Kamal. The number of days, Bimal will take to do the same piece of work, is (a) 10 days      (b) 10 1/2 days     (c) 12 days         (d) 14 days

Q4. A and B together can complete a piece of work in 12 days, B and C can do it in 20 days and C and A can do it

1. 