Trigonometry

What indicates an acute triangle in terms of side lengths?

The c² value is less than a + b.

What indicates an obtuse triangle in terms of side lengths?

The c² value is more than a + b.

What is the relationship between the sides of a 45-45-90 triangle?

If x is the length of each leg, then the hypotenuse c = x√2.

In a 30-60-90 triangle, what are the side length ratios?

X : x√3 : 2x, where x is the shorter leg.

What is the abbreviation for a missing angle in trigonometry?

Theta (θ).

What does 'adjacent' refer to in trigonometric ratios?

The leg that touches the angle θ.

What is the definition of sine(θ)?

sin(θ) = opposite/hypotenuse.

What is the definition of cosine(θ)?

cos(θ) = adjacent/hypotenuse.

What is the definition of tangent(θ)?

tan(θ) = opposite/adjacent.

What is the Law of Sines formula?

sinA/a = sinB/b = sinC/c.

What is the Law of Cosines formula?

c² = a² + b² - 2ab cos(C).

What is the Pythagorean Theorem formula?

a² + b² = c².

What type of triangle is indicated when c² = a² + b²?

Right triangle.