In Chapter 9, "Some Applications of Trigonometry," Class 10 students will explore how trigonometry can be applied to calculate the height and distance of various objects without direct measurement. Historically, astronomers used trigonometry to calculate the distances between planets, Earth, and stars. In modern times, it is commonly used in geography and navigation to determine the latitude and longitude of specific locations.
This chapter will cover key concepts such as heights and distances, the line of sight, the angle of elevation, the horizontal line, and the angle of depression.
The horizontal level is the horizontal line through the eye of the observer.
The line which is drawn from the eyes of the observer to the point being viewed on the object is known as the line of sight.
ΔABC is a right angled triangle where is AB is the perpendicular, AC is the hypotenuse, and BC is the base.
Then,
Trigonometrical Identities:
Q2: When a boy looks from the foot and the top of a tower at the roof of a building, the angles of elevation and depression are $2$27^{o} and 63^{o}, The height of this building is 40m, then calculate the height of the tower given that tan 630 =2.
Ans: Let the tower be AB
Let the building of height 40m be CD
In the given triangle ACD, AC/DC = cot 270
= cot (9063)
AC/40 = tan 630 = 2
AC = 80m
Now, DE = AC = 80m
Also, in triangle BED, tan 630 = BE/DE
2= BE/80
Therefore, BE = 160 m
Therefore, the height of the tower can be calculated as AE + EB
= 40 +160 = 200m
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1. What are the formulas for the angle of elevation and angle of depression in trigonometry? 
2. What is the definition of Harmonic Progression (H.P) in trigonometry? 
3. Can you provide some height and distance formulas for trigonometric ratios? 
4. How can trigonometry be applied in reallife situations? 
5. What are some common applications of trigonometry in Class 10 mathematics? 

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