Understanding Right-Angled Triangles

The video tutorial introduces trigonometry, focusing on right-angled triangles and the Pythagorean Theorem. It explains the sides of a triangle, such as the hypotenuse, adjacent, and opposite sides, and how to calculate the length of a side using the theorem. The tutorial includes examples to demonstrate the application of the theorem in solving problems involving right-angled triangles.

What is the primary focus of trigonometry as introduced in the video?

• The study of circles

• The geometry of triangles

• The calculation of areas

• The measurement of angles

Who is the ancient Greek figure associated with the theorem discussed in the video?

• Pythagoras

• Socrates

• Euclid

• Archimedes

What type of triangle is primarily discussed in the video?

• Scalene triangle

• Isosceles triangle

• Equilateral triangle

• Right-angled triangle

What is the longest side of a right-angled triangle called?

• Opposite

• Adjacent

• Base

• Hypotenuse

What is the name of the angle often used in trigonometry, represented by a Greek letter?

• Alpha

• Beta

• Gamma

• Theta

According to Pythagoras' Theorem, what is the relationship between the sides of a right-angled triangle?

• The sum of the two shorter sides equals the hypotenuse

• The product of the two shorter sides equals the hypotenuse

• The difference between the squares of the two shorter sides equals the hypotenuse

• The sum of the squares of the two shorter sides equals the square of the hypotenuse

In the example with a 3-4-5 triangle, what is the length of the hypotenuse?

• 5 units

• 6 units

• 4 units

• 3 units

What is the area of the square on the hypotenuse in the 3-4-5 triangle example?

• 9

• 16

• 25

• 20

How can Pythagoras' Theorem be applied to any right-angled triangle?

• By using the product of the sides

• By using the sum of the angles

• By using the sum of the sides

• By using the sum of the squares of the two shorter sides

In the example with sides 9 and 12, what is the length of the hypotenuse?

• 15

• 18

• 21

• 24