Solving Acute or Obtuse Triangles

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What is the Sine Rule?

Back

The Sine Rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It is expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Front

What is the Cosine Rule?

Back

The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab*cos(C).

Front

When should you use the Sine Rule?

Back

Use the Sine Rule when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When should you use the Cosine Rule?

Back

Use the Cosine Rule when you know two sides and the included angle (SAS) or all three sides (SSS) to find an angle.

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How many parts do you need to equate when using the Sine Rule?

Back

You need to equate 2 parts (fractions) when using the Sine Rule.

Front

What is the relationship between angles and sides 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 Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

How do you find an angle using the Sine Rule?

Back

To find an angle using the Sine Rule, rearrange the formula to sin(A) = a * sin(B) / b, then use the inverse sine function.

Front

How do you find a side using the Cosine Rule?

Back

To find a side using the Cosine Rule, rearrange the formula to a = √(b² + c² - 2bc*cos(A)).

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.