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Numerical Aptitude (Chapter: Trigonometry)

Trigonometry

In the triangles, particularly in right angle triangles, let us take some example from our surrounding where right triangles can be imagined to be formed. For example:-

1. Suppose the students of a school are visiting Qutub Minar. Now, if a student is looking at the top of the Minar, a right triangle can be imagined to be made, as shown in figure below. Can the student find out the height of the Minar, without actually measuring it?

2. Suppose a girl is sitting on the balcony of her house located on the bank of a river. She is looking down at a flower pot placed on a stair of a temple situated nearby on the other bank of the river. A right triangle is imagined to be made in this situation as shown in Figure below. If you know the height at which the person is sitting, can you find the width of the river ?

3. Suppose a hot air balloon is flying in the air. A girl happens to spot the balloon in the sky and runs to her mother to tell her about it. Her mother rushes out of the house to look at the balloon. Now when the girl had spotted the balloon initially it was at point A. When both the mother and daughter came out to see it, it had already traveled to another point B. Can you find the altitude of B from the ground?

In all the situations given above, the distances or heights can be found by using some mathematical techniques, which come under a branch of mathematics called ‘trigonometry’. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). In fact, trigonometry is the study of relationships between the sides and angles of a triangle. The earliest known work on trigonometry was recorded in Egypt and Babylon. Early astronomers used it to find out the distances of the stars and planets from the Earth. Even today, most of the technologically advanced methods used in Engineering and Physical Sciences are based on trigonometrically concepts.

Trigonometric Ratios

The ratio of the sides of a right-angled triangle with respect to its angles are called trigonometric ratios. Left us draw a right angle triangle say triangle ABC show in figure.

:: Home Assignment for Practice ::

1. Rakesh saw an aeroplane flying horizentally 1 km above the ground. The angle of elevation was 60^0. What was the distance of the aeroplane from Rakesh at that moment?

(a) 1/Ö3 km
(b) Ö3 km
(c) 2/Ö3 km
(d) None of these

2. The angle of elevation of the top of a tower at a point on the ground is 30o. On walking 24 m towards the tower, the angle of elevation becomes 60^o. Find the height of the tower.

(a) 2.076 m
(b) 20.67 m
(c) 2 m
(d) None of these

3. A man wishes to find the height of a flagpost which stands on a horizontal plane; at a point on this plane he finds the angle of elevation of the top of the flagpost to be 45o. On walking 30 meters towards the town he finds the corresponding angle of elevation to be 60o. Find the height of the flagpost.

(a) 69 m
(b) 70 m
(c) 71 m
(d) 74 m

4. The shadow of a vertical pole in of its height. Find the angle of elevation.

(a) 30^o
(b) 45^o
(c) 60^o
(d) 90^o

5. A man on the top of a town, standing on the seashare finds that a boat coming towardes him takes 10 minutes for the angle of depression to change from 30o to 60o^o Find the time taken by the boat to reach the shore from the position.

(a) 5 min
(b) 10 min
(c) 8 min
(d) 15 min

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