9. Some Applications of Trigonometry

Class X

Exercise 9.1

NCERT Textbook Solution

Learning Points

• Angle of Elevation
• Angle of Depression

Angle of Elevation

The angle between line of sight and horizontal level when the observer is below the object is said to be angle of elevation.

Angle of Depression

The angle between line of sight and horizontal level when the observer is above the object is said to be the angle of depression.

Exercise 9.1

Q.No.1. 

 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. Find the height of the pole, if the angle made by the rope with the ground level is 30° (see Fig. 9.11).

Fig. 9.11

Solution:

From question it is clear that

Angle of Elevation = Ө = 30°

Height of the pole = AB = ?

Now applying trigonometric ratio sin𝞱

From figure it is clear that

sin𝞱 = AB/AC

Now putting the value of 

1/2 = AB/20

AB = 10 m Ans.

1. Real Numbers

Learning points in the point of view of 

Exercise 1.1 Class X Mathematics

• Euclid Division Lemma
• Euclid Division Algorithm
• Even Positive Integers
• Odd Positive Integers

Euclid Division Lemma

If a positive integer a is divided by b and remainder r is greater than or equal to zero but less than b. This statement is said to be Euclid Division Lemma.

In Mathematically it can be written as

a = bq + r

0≤ r⋖b

Euclid Division Algorithm

The stepwise calculation to find out the HCF of two positive integers by applying Euclid Division Lemma is said to be Euclid Division Algorithm.

Even Positive Integers

The positive integers which are completely divisible by 2 is said to be even positive integers.

Odd Positive Integers

The positive integers which are not completely divisible by 2 is said to be odd positive integers. 

Now we are able to solve the questions of Exercise 1.1