Solving for Unknowns in Triangles

Front

What is the Cosine Rule used for in triangles?

Back

The Cosine Rule is used to find a side or angle in a triangle when you know two sides and the included angle, or all three sides.

Front

What is the Sine Rule used for in triangles?

Back

The Sine Rule is used to find unknown sides or angles in a triangle when you know two angles and one side, or two sides and a non-included angle.

Front

What is the Tangent Rule used for in triangles?

Back

The Tangent Rule is used to find an angle when you know the lengths of the opposite and adjacent sides.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (Hyp) is equal to the sum of the squares of the lengths of the other two sides (opp and adj): Hyp² = opp² + adj².

Front

How do you calculate an angle using the Cosine Rule?

Back

To calculate an angle using the Cosine Rule, rearrange the formula: cos(A) = (b² + c² - a²) / (2bc) and use the inverse cosine function.

Front

How do you calculate an angle using the Sine Rule?

Back

To calculate an angle using the Sine Rule, use the formula: sin(A)/a = sin(B)/b = sin(C)/c and rearrange to find the angle.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side; conversely, the smaller the angle, the shorter the opposite side.

Front

What is the formula for the Sine Rule?

Back

The Sine Rule is given by: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the sides of the triangle and A, B, and C are the opposite angles.

Front

What is the formula for the Cosine Rule?

Back

The Cosine Rule is given by: c² = a² + b² - 2ab * cos(C), where a, b, and c are the sides of the triangle and C is the included angle.

Front

How do you find the length of a side using the Pythagorean Theorem?

Back

To find the length of a side, rearrange the Pythagorean Theorem: a = √(Hyp² - opp²) or b = √(Hyp² - adj²).