TRIGONOMETRY

 Learning outcomes 

After learning this topic, students will be able to:

1)Identify a 45°–45°–90° triangle and recognize it as an isosceles right-angled triangle.

2) State and explain that the ratio of the sides of a 45°–45°–90° triangle is 1 : 1 : √2.

3) Apply the Pythagoras theorem to verify the side ratio of a 45°–45°–90° triangle.

4) Calculate the length of unknown sides of a 45°–45°–90° triangle using the ratio 1 : 1 : √2.

5) Understand the meaning of trigonometry as the study of the relationship between the sides and angles of triangles.

6) Identify right-angled triangles as the triangles in which trigonometric ratios are applicable.

Video

Trigonometry

YouTube video:

Notes

Introduction to Trigonometry

Trigonometry is the branch of mathematics that studies the relationship between the angles and sides of triangles.

The word Trigonometry comes from two Greek words:

Trigonon – meaning triangle

Metron – meaning measure

So, trigonometry literally means measurement of triangles.

Trigonometry is mainly applicable to right-angled triangles, that is, triangles that have one angle equal to 90°.

A triangle whose angles are 45°, 45°, and 90° is called a 45°–45°–90° triangle.

Since two angles are equal, the sides opposite to those angles are also equal. Therefore, it is an isosceles right-angled triangle.

If the two equal sides are taken as 1 unit each, then by Pythagoras theorem,

Therefore, the ratio of the sides of a 45°–45°–90° triangle is:

1 : 1 : √2

This means:

The two shorter sides are equal.

The hypotenuse is √2 times the length of each shorter side.

Ppt 

Ppt

MCQ

1. In a triangle with angles 45°, 45°, and 90°, the ratio of the sides is:

A) 1 : 2 : 3

B) 1 : 1 : √2

C) 1 : √2 : 2

D) 2 : 3 : √5

2. If the equal sides of a 45°–45°–90° triangle are 5 cm each, the hypotenuse is:

A) 5√2

B) 5

C) 25

D) 10

3. A right-angled triangle has angles 45°, 45°, and 90°. Such a triangle is called:

A) Scalene triangle

B) Equilateral triangle

C) Isosceles right triangle

D) Obtuse triangle

4. If the hypotenuse of a 45°–45°–90° triangle is 10 cm, each shorter side is:

A)5√2

B) 10√2

C) 10

D)5

5. If the sides of a triangle are in the ratio 1 : 1 : √2, the angles of the triangle are:

A) 30°, 60°, 90°

B) 45°, 45°, 90°

C) 60°, 60°, 60°

D) 30°, 45°, 105°

6.A right-angled triangle has two equal sides. The angles of the triangle are:

A) 30°, 60°, 90°

B) 45°, 45°, 90°

C) 60°, 60°, 60°

D) 30°, 30°, 120°

7.If the length of one leg of a 45°–45°–90° triangle is 8 cm, the hypotenuse is:

A) 8√2

B) 4√2

C) 8

D) 16

8. If the hypotenuse of a 45°–45°–90° triangle is 6√2 cm, each of the other sides is:

A) 3 cm

B) 6 cm

C) 12 cm

D) 6√2 cm

9.In a 45°–45°–90° triangle, the two smaller sides are:

A) unequal

B) equal

C) three times each other

D) unrelated

10. For which type of triangle trigonometry applicable?

A) right angled triangle 

B) isosceles triangle 

C) equilateral triangle 

D) all the above 

MCQ in Google form

https://docs.google.com/forms/d/e/1FAIpQLSezjVd6la7aE2DMO9_7WmfynYzRhlA4tR9u7QLmpSf_7KqT0w/viewform?usp=dialog