Trigonometric Relationships in Right Triangles

This video tutorial covers trigonometric relations in right triangles, focusing on sine, cosine, and tangent functions. It explains the concepts of angles and how these functions relate to the sides of a triangle. The tutorial includes practical applications, solving real-world problems using these trigonometric functions, and demonstrates how to handle complex problems involving multiple triangles.

What is the defining characteristic of a right triangle?

• It has three equal sides.

• It has an obtuse angle.

• It has an angle of 90 degrees.

• It has two acute angles.

In a right triangle, what is the sine of an angle defined as?

• Opposite side over hypotenuse

• Adjacent side over opposite side

• Adjacent side over hypotenuse

• Hypotenuse over opposite side

Which trigonometric function is defined as the adjacent side over the hypotenuse?

• Cosine

• Sine

• Tangent

• Secant

If the opposite side of an angle in a right triangle is 5 and the hypotenuse is 13, what is the sine of the angle?

• 5/13

• 12/13

• 5/12

• 13/5

A car travels 80 meters up a hill inclined at 30 degrees. What is the height it reaches?

• 20 meters

• 80 meters

• 60 meters

• 40 meters

What trigonometric function would you use to find the height of a building if you know the length of its shadow and the angle of elevation?

• Sine

• Secant

• Tangent

• Cosine

If a building casts a shadow of 30 meters when the angle of elevation of the sun is 60 degrees, what is the height of the building?

• 15 meters

• 30√3 meters

• 15√3 meters

• 30 meters

In a right triangle, if the hypotenuse is 17 and one of the angles is 60 degrees, what is the length of the side adjacent to the 60-degree angle?

• 8.5

• 17√3

• 17

• 8.5√3

What is the cosine of a 60-degree angle in a right triangle?

• 1

• 0

• √3/2

• 1/2

If the opposite side of a 30-degree angle in a right triangle is 8√3, what is the hypotenuse?

• 16√3

• 8√3

• 16

• 8