Retake: Unit 3 Laws, Area, and Trig Identities

Front

What is the formula for the area of a triangle?

Back

The area of a triangle can be calculated using the formula: \( A = \frac{1}{2} \times base \times height \).

Front

How do you find the area of a triangle given three sides?

Back

You can use Heron's formula: \( A = \sqrt{s(s-a)(s-b)(s-c)} \), where \( s = \frac{a+b+c}{2} \) is the semi-perimeter.

Front

What is the Law of Sines?

Back

The Law of Sines states that \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \), where \( a, b, c \) are the sides of a triangle and \( A, B, C \) are the angles opposite those sides.

Front

What is the Law of Cosines?

Back

The Law of Cosines states that \( c^2 = a^2 + b^2 - 2ab \cos(C) \), which relates the lengths of the sides of a triangle to the cosine of one of its angles.

Front

How do you calculate the angle of elevation?

Back

The angle of elevation is calculated using the tangent function: \( \tan(\theta) = \frac{opposite}{adjacent} \).

Front

What is the relationship between the sides and angles in a right triangle?

Back

In a right triangle, the sides are related to the angles through trigonometric ratios: sine, cosine, and tangent.

Front

What is the definition of a trigonometric identity?

Back

A trigonometric identity is an equation that is true for all values of the variable where both sides are defined.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.

Front

How do you find the area of a triangle using two sides and the included angle?

Back

The area can be calculated using the formula: \( A = \frac{1}{2}ab \sin(C) \), where \( a \) and \( b \) are the sides and \( C \) is the included angle.

Front

What is the definition of secant in trigonometry?

Back

Secant is defined as \( \sec(x) = \frac{1}{\cos(x)} \).