Properties of 30-60-90 and 45-45-90 Triangles

This video tutorial covers the basics of trigonometry, focusing on the Pythagorean Theorem and special right triangles. It begins with an introduction to trigonometry, emphasizing its importance in understanding the relationships between the sides and angles of triangles. The tutorial then delves into the Pythagorean Theorem, providing examples to illustrate its application. Following this, the video explores special right triangles, specifically 45-45-90 and 30-60-90 triangles, explaining their properties and solving related problems.

What is the primary focus of trigonometry?

• The relationship between sides and angles of triangles

• The study of circles

• The calculation of areas

• The measurement of angles in polygons

In a right triangle, what is the side opposite the right angle called?

• Base

• Opposite

• Adjacent

• Hypotenuse

What is the formula for the Pythagorean Theorem?

• a + b = c^2

• a^2 = b^2 + c^2

• a^2 + b^2 = c^2

• a^2 + b^2 = c

If a right triangle has legs of 3 and 4, what is the length of the hypotenuse?

• 7

• 5

• 8

• 6

In a 45-45-90 triangle, how do you find the hypotenuse if you know the length of a leg?

• Multiply the leg by √2

• Multiply the leg by √3

• Divide the leg by √3

• Divide the leg by √2

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 5?

• 10

• 5√2

• 7

• 5√3

In a 30-60-90 triangle, what is the relationship between the hypotenuse and the short leg?

• The hypotenuse is three times the short leg

• The hypotenuse is half the short leg

• The hypotenuse is the same as the short leg

• The hypotenuse is twice the short leg

How do you find the long leg in a 30-60-90 triangle if you know the short leg?

• Multiply the short leg by √2

• Multiply the short leg by √3

• Divide the short leg by √2

• Divide the short leg by √3

If the short leg of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

• 4

• 12

• 8

• 6

In a 30-60-90 triangle, if the long leg is 6, what is the length of the short leg?

• 6

• 4

• 3

• 5