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ACT Math: Tips for solving triangle problems?

When it comes to the math section on the ACT, I kind of struggle with triangle problems. Any advice or resources on how to tackle these problems?

10 months ago

Triangle problems are a common topic on the ACT math section, and understanding a few key concepts and strategies should help you navigate them more confidently. Here are some tips and techniques to consider when solving triangle problems:

1. Know the basic triangle properties:

- The sum of a triangle's interior angles is always 180 degrees.

- For right triangles, the Pythagorean theorem (a² + b² = c²) applies, where "a" and "b" are the legs and "c" is the hypotenuse.

2. Understand special types of triangles:

- Equilateral triangles have all sides and angles equal, and each angle measures 60 degrees.

- Isosceles triangles have two equal sides and two equal angles.

- Scalene triangles have no equal sides or angles.

- Right triangles have one 90-degree angle.

3. Learn and apply trigonometry concepts:

For right triangles, know the basic trigonometric functions and their relationships:

- sine (opposite/hypotenuse)

- cosine (adjacent/hypotenuse)

- tangent (opposite/adjacent)

A helpful acronym to remember this is "SOHCAHTOA."

4. Use similar triangles:

Triangles are similar if they have the same shape but not necessarily the same size. In similar triangles, corresponding angles are equal, and corresponding sides are proportional. You can use this property to solve problems that involve relationships between the sides and missing length values.

5. Apply the 30-60-90 and 45-45-90 special right triangles rules:

- 30-60-90 triangles have sides with a ratio of 1:sqrt(3):2.

- 45-45-90 triangles have sides with a ratio of 1:1:sqrt(2).

6. Utilize the Law of Sines and Law of Cosines:

These are used for non-right triangles to find unknown angles and side lengths.

- Law of Sines: (a/sinA) = (b/sinB) = (c/sinC)

- Law of Cosines: c² = a² + b² - 2ab(cosC)

As you practice, focus on recognizing which concepts apply to the problem at hand and developing a strategy to efficiently tackle it. Some free resources to help you practice include the official ACT website (www.act.org) and Khan Academy (www.khanacademy.org). Happy studying!

10 months ago

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