Trigonometry - Quantitative Aptitude

Q11. The angle of elevation of a tower from a distance 100m from its foot is 30⁰. The height of the tower is
(a) ⁶⁵/_√2 m
(b) ⁷⁵/_√2 m
(c) ⁹⁰/_√3 m
(d) ¹⁰⁰/_√3 m

Q12. At an instant, the length of the shadow of a pole is √3 times the height of the pole. The angle of the elevation of the sun is
(a) 30⁰
(b) 45⁰
(c) 60⁰
(d) 90⁰

Q13. The angles of depression of two ships from the top of a light house are 45⁰ and 30⁰ towards east. If the ships are 100 m apart, the height of the light house is
(a) 20(√2 + 1)
(b) 30(√3 + 1)
(c) 40(√2 + 1)
(d) 50(√3 + 1)

Q14. From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30⁰ and 60⁰ respectively. What is the height of the tower ?
(a) 45 m
(b) 50 m
(c) 60 m
(d) 70 m

Q15. If Sin 32⁰ = x, then Cos 58⁰ = ?
(a) x
(b) 1/x
(c) x²
(d) x³

Q16. Two men are opposite sides of a tower. They measure the angles of evaluation of the top of the tower as 30⁰ and 45⁰ respectively. If the height of the tower is 100 m, find the distance between the two men.
(a) 80(√2 + 1) m
(b) 90(√3 + 1) m
(c) 100(√3 + 1) m
(d) 120(√5 + 1) m

Q17. √(1+SinA)/(1-SinA) = ?
(a) SecA + SinA
(b) CosA + SinA
(c) SecA + tanA
(d) SecA + CosA

Q18. The angle of elevation of a ladder leaning against a wall is 45⁰ and the foot of the ladder is 6m away from the wall. The length of the ladder is
(a) 4√2 m
(b) 5√3 m
(c) 6√2 m
(d) 7√3 m

Q19. tan35⁰tan40⁰tan45⁰tan50⁰tan55⁰ = ?
(a) 1
(b) 2
(c) 4
(d) 5

Q20. The shadow of a building is 20m long when the angle of elevation of the Sun is 45⁰. Find the height of the building.
(a) 15 m
(b) 18 m
(c) 20 m
(d) 23 m

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