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NCERT Solutions For Class 10 Maths Chapter 8 PDF: Introduction To Trigonometry

In this chapter, you will be studying about some ways in which trigonometry is used in the life around trigonommetry. Trigonometry is one of the most ancient subjects studied by scholars all over the world. As we have said in Chapter 8, trigonometry was invented because its need arose in astronomy. Since then the astronomers have used it, for instance, to calculate distances from imate Earth to the planets and stars.

Trigonometry is also used in geography and in navigation. The knowledge of trigonometry is used to construct maps, determine the position of an island in relation to the longitudes and latitudes. Surveyors have used trigonometry trgionometry centuries. During the survey inthe highest mountain in the world was discovered.

From a distance of over km, the peak trigonometry 10th ncert pdf image observed from six different stations.

Inthis peak was named after Sir George Everest, who had A Theodolite commissioned and first used the giant Surveying instrument, which trkgonometry based theodolites see the figure alongside. The trkgonometry the Principles of trigonometry, is theodolites are now on display in the used for measuring angles trigono,etry a Museum of the Survey of India in rotating telescope Dehradun.

In this chapter, we will see how trigonometry is used for finding the heights and distances of various objects, without actually measuring. The student is looking at the top of the minar. The angle BAC, so formed by the line of sight with the horizontal, is called the angle of elevation of the top of the minar from the eye of the student.

Thus, the line of sight is the line drawn from the eye of an observer to the point trigonometry 10th ncert pdf image the object viewed by the observer. The angle of elevation of the point trigonometry 10th ncert pdf image is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.

Now, consider the situation given in Trigonometry 10th ncert pdf image. The girl sitting on the balcony is looking down at a flower pot placed on a stair of the temple. In this case, the line of sight is below the horizontal level. The angle so formed rrigonometry the line of sight with the horizontal is called the angle of depression. Thus, the angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.

Are they angles of elevation or angles imaage depression? Let us refer to Fig. Trigonometry 10th ncert pdf image you want to find the height CD of the minar without actually measuring it, what information do trigonometry 10th ncert pdf image need? Assuming that the above trigonometry 10th ncert pdf image conditions Trigonometry Class 10th Ncert Pdf Github are known, how can we determine the height of the minar?

Now, which of the trigonometric ratios can we use? Which one of them has the two values that we have and the one we need to determine? Example 1 : A tower stands vertically on the ground. Find the height of trigonometry 10th ncert pdf image tower. Solution : Trigonometry 10th ncert pdf image let us draw a simple diagram to represent the problem see Fig. We need to determine the height of the tower, i. Also, ACB is a triangle, right-angled at B.

AB Fig. Trigonlmetry 2 : An jmage has to repair an electric fault on a pole of height 5 m. She needs iimage reach a point 1. Also, how far from the foot of the pole odf she place the foot of the ladder? Solution : In Fig.

Here, BC represents the ladder. We need to find its length, i. Now, can you think which trigonometic ratio should we consider? Example 3 : An observer 1.

What is the height of the chimney? In this case, ADE is a triangle, right-angled at E and trigonometry 10th ncert pdf image are required to find the height of the chimney. Let us choose the tangent of the angle of elevation. Find the length of the flagstaff and the distance of the building from the point P. Pdg are required to trgionometry the length of the flagstaff, i. According to the question, DB is 40 m longer than BC.

Find the height of the multi-storeyed building and the bcert between the two buildings. We are interested to determine the height of the multi-storeyed building, i.

Look at the figure carefully. If the bridge is at a height of 3 m from the banks, find the trigonometry 10th ncert pdf image of the river. Solution : In Fig 9. P is a point on the bridge at a height of 3 m, i. We are interested to ikage the width Fig. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground.

The distance between the foot of the tree to the trogonometry where the top Fig. Find the height of the tree. A contractor plans to install two slides for the children to play in a park. For the children trigonometry 10th ncert pdf image the age of 5 years, she prefers to have a slide whose top is at a height of 1. What should be the length of the slide Ncert Science Class 10th Pdf Images in each case?

A kite is flying at imafe height of imate m above the ground. The string yrigonometry to the kite is temporarily tied to a point on the ground. Find the length 1th the string, assuming that there is no slack in the string. Find the distance he walked towards the building. Ncfrt statue, 1. Find the height of the pedestal. If the tower is 50 m high, find the height of the building. Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide.

Find the height of the poles and the distances of the point from the poles. A TV tower stands vertically on a bank of a canal. Find the height of the tower and the width of Fig. Determine the height of the tower. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. Pxf the distance travelled by the balloon during the interval.

A straight highway leads to the foot of a tower. Find the time taken by the car to reach the foot of the tower from this point. The angles of elevation of the top of a tower from two points at a distance of trigonometdy m and 9 m from the base of the tower and in the same straight line with it are complementary.

Prove that the height of the tower is 6 m. The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios. Open navigation menu. Close suggestions Search Search. User Settings.

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Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. Now let us explain the process, we have just discussed, by solving some problems. Documents Similar To Chapter 9. Hazem Emam.

Chapter Circles. In order to achieve the maximum marks in exams, all students need to read the NCERT books thoroughly and solve the exercise questions given at the end of every chapter. Keep visiting Jagran Josh to get the latest updates and reliable study material for preparations of all school and board examinations. Chapter 1: Real Numbers. At last, you will also establish some relationships among these trigonometric ratios which are termed as trigonometric identities.

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