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To find the missing lengths of a 30-60-90 triangle, follow these steps:
1. Identify the triangle: Recognize that you are working with a 30-60-90 triangle, which is a special right triangle.
2. Understand the ratios: In a 30-60-90 triangle, the side lengths are in a specific ratio. The ratio is 1:√3:2, where the length of the shortest side (opposite the 30-degree angle) is represented as 'x', the length of the longer leg (opposite the 60-degree angle) is 'x√3', and the length of the hypotenuse (opposite the 90-degree angle) is '2x'.
3. Determine the known lengths: Identify the given length of any one side of the triangle. This will allow you to calculate the lengths of the other two sides.
4. Calculate the missing lengths: Use the known length and the ratios of the 30-60-90 triangle to find the missing lengths.
- If the shortest side (opposite the 30-degree angle) is given, the longer leg (opposite the 60-degree angle) is found by multiplying the given length by √3, and the hypotenuse (opposite the 90-degree angle) is found by multiplying the given length by 2.
- If the longer leg (opposite the 60-degree angle) is given, divide the given length by √3 to find the length of the shortest side (opposite the 30-degree angle), and multiply the given length by 2/√3 to find the length of the hypotenuse.
- If the hypotenuse (opposite the 90-degree angle) is given, divide the given length by 2 to find the length of the shortest side (opposite the 30-degree angle), and divide the given length by 2√3 to find the length of the longer leg (opposite the 60-degree angle).
By understanding the ratios of a 30-60-90 triangle and utilizing the known lengths, you can calculate the missing lengths of the triangle.
These videos are designed to review and reteach high school Geometry content. My videos cover…
Points, Lines, and Planes,
Angles and Angle Relationships,
Triangles,
Quadrilaterals,
Circles,
Similarity and Proportions,
Congruent Figures,
Coordinate Geometry,
Transformations,
Area and Perimeter,
Volume and Surface Area,
Right Triangles and Trigonometry,
Geometric Proofs,
Constructions,
Non-Euclidean Geometries.
I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: [ Ссылка ]
Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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