Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Important Definitions & Formulas: Some Application of Trigonometry
Important Definitions & Formulas: Some Application of Trigonometry | Mathematics (Maths) Class 10 PDF Download
Introduction
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.
Horizontal Level
The horizontal level is the horizontal line through the eye of the observer.
Line of Sight
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.
Angle of Elevation
The Angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e., the case when we raise our head to look at the object.
Angle of Depression
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.e., the case when we lower our head to look at the point being viewed.
Height and Distance Formulas for Trigonometric ratio
ΔABC is a right angled triangle where is AB is the perpendicular, AC is the hypotenuse, and BC is the base.
Then,
- Sin θ = AB/AC
- Cos θ = BC/AC
- Tan θ = AB/BC
- Cosec θ = AC/AB
- Sec θ = AC/BC
- Cot θ = BC/AB
Trigonometrical Identities:
- sin2θ + cos2 θ = 1
- 1 + tan2θ = sec2 θ
- 1 + cot2θ = cosec2 θ
Some Examples Using Above Formulas
Q1: Adam is standing in the Sun. He is 6ft tall and is casting a shadow of 4ft. A flag is also present near the man casting a shadow of 36ft. Calculate the height of the flag.
Ans: The angle of elevation for the Sun will be the same for both the cases.
Therefore, the ratio of object to shadow will be the same for both the cases as per the proportionality rule.
Object height/ Shadow height = 6/ 4 = H /36
Therefore, H = 54 ft = Height of the flag
Ans: The angle of elevation for the Sun will be the same for both the cases.
Therefore, the ratio of object to shadow will be the same for both the cases as per the proportionality rule.
Object height/ Shadow height = 6/ 4 = H /36
Therefore, H = 54 ft = Height of the flag
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 27o and 63o, 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 (90-63)
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
The document Important Definitions & Formulas: Some Application of Trigonometry | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Important Definitions & Formulas: Some Application of Trigonometry - Mathematics (Maths) Class 10
| 1. What are the formulas for the angle of elevation and angle of depression in trigonometry? |  |
Ans. The formula for the angle of elevation is tan θ = opposite/adjacent, and the formula for the angle of depression is tan θ = opposite/adjacent.
| 2. What is the definition of Harmonic Progression (H.P) in trigonometry? | |
Ans. Harmonic Progression (H.P) is a sequence of numbers in which the reciprocals of the terms form an arithmetic progression.
| 3. Can you provide some height and distance formulas for trigonometric ratios? | |
Ans. Some height and distance formulas for trigonometric ratios include sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent.
| 4. How can trigonometry be applied in real-life situations? | |
Ans. Trigonometry is commonly used in fields such as engineering, physics, and architecture for tasks like measuring distances, calculating angles, and determining heights of objects.
| 5. What are some common applications of trigonometry in Class 10 mathematics? | |
Ans. Some common applications of trigonometry in Class 10 mathematics include solving problems related to angles of elevation and depression, calculating distances and heights using trigonometric ratios, and understanding harmonic progression.
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