Trigonometry and Triangle Properties

This video tutorial covers lesson eight on trigonometry, focusing on the characteristics of trigonometric functions such as sine, cosine, and tangent. It explains the relationships between these functions, particularly in complementary angles, and provides a graphical approach to understanding these concepts. The video also includes a variety of mixed word problems to apply these trigonometric principles in real-world scenarios. Advanced problems are tackled towards the end, offering a comprehensive understanding of trigonometry applications.

What is the relationship between the sine of an angle and the cosine of its complement?

• They are unrelated.

• They are reciprocals.

• They are inverses.

• They are equal.

How are the tangent of an angle and the tangent of its complement related?

• They are equal.

• They are inverses.

• They are reciprocals.

• They are unrelated.

In a right triangle, if the sine of an angle is 0.6, what is the cosine of its complement?

• 0.4

• 0.6

• 0.8

• 1.0

How do you find the missing side of a right triangle if the sine button on your calculator is broken?

• Use the Pythagorean theorem.

• Use the secant of the angle.

• Use the tangent of the angle.

• Use the cosine of the complement angle.

If a tree casts a shadow of 150 feet and the angle of elevation to the top is 50 degrees, how tall is the tree?

• 115 feet

• 179 feet

• 129 feet

• 200 feet

What is the angle of elevation of a skateboard ramp that is 6 feet long and 3 feet high?

• 15 degrees

• 60 degrees

• 30 degrees

• 45 degrees

What is the perimeter of a trapezoid if one side is 8, another is 2, and the other two sides are 9.9 and 7.8?

• 25.7

• 31.7

• 29.7

• 27.7

In a 30-60-90 triangle, if the longer leg is 15 meters, what is the length of the shorter leg?

• 20 meters

• 5√3 meters

• 10 meters

• 15 meters

What is the length of each side of a square if its diagonal is 10 centimeters?

• 10 cm

• 7 cm

• 12 cm

• 5√2 cm

In an equilateral triangle with sides of 18 meters, what is the length of the altitude?

• 9 meters

• 9√3 meters

• 18 meters

• 18√3 meters