Exploring Trigonometric Ratios in Geometry

The video tutorial introduces trigonometric ratios, focusing on sine, cosine, and tangent. It explains how these ratios relate the sides of a right triangle to its angles. The tutorial demonstrates how to calculate these ratios and apply them to find missing sides in triangles. It also covers the concept of angle of elevation with practical examples. The video concludes with practice problems to reinforce the concepts learned.

What does a trigonometry ratio compare in a right triangle?

• The length of the sides to the angles of the triangle

• The length of one side to the length of another side

• The area of the triangle to the perimeter of the triangle

• The length of the sides to the square of the hypotenuse

How is the sine of an angle in a right triangle defined?

• Opposite side over hypotenuse

• Opposite side over adjacent side

• Hypotenuse over opposite side

• Adjacent side over hypotenuse

What is the sine of an angle primarily used for in trigonometry?

• To find the length of the hypotenuse

• To calculate the area of the triangle

• To find the length of the side opposite the angle

• To measure the angle itself

What is the correct representation of cosine in a right triangle?

• Adjacent side over opposite side

• Opposite side over hypotenuse

• Adjacent side over hypotenuse

• Hypotenuse over adjacent side

In trigonometry, what does tangent compare?

• Opposite side to adjacent side

• Hypotenuse to opposite side

• Adjacent side to hypotenuse

• Opposite side to hypotenuse

What mnemonic helps remember the trigonometry ratios?

• SOHCAHTOA

• PEMDAS

• ROYGBIV

• None of the above

How do you find the length of a side in a right triangle using trigonometry ratios?

• By adding the lengths of the other two sides

• By applying the Pythagorean theorem

• By using trigonometry ratios like sine, cosine, or tangent

• By dividing the angle by the length of another side

What is the angle of elevation in trigonometry?

• The angle formed by the vertical line and the line of sight to an object

• The angle between the opposite side and the hypotenuse

• The angle formed by the line of sight and the horizontal line from the observer

• The angle between the hypotenuse and the adjacent side

Which trigonometry ratio is used when you have opposite and adjacent sides?

• Tangent

• Cotangent

• Cosine

• Sine

How can trigonometry be applied in real life?

• To measure the depth of a lake

• To calculate the height of a building

• To find the distance between two points on a map

• All of the above