Solve real-world and mathematical geometric problems using algebraic methods.

9.3.4.1Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.9.3.4.2Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.9.3.4.3Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.9.3.4.4Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.9.3.4.5Know the equation for the graph of a circle with radius r and center (h, k), (x - h)^2 + (y - k)^2 = r^2, and justify this equation using the Pythagorean Theorem and properties of translations.9.3.4.6Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90 degrees, to solve problems involving figures on a coordinate grid.9.3.4.7Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.
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