SAT Math: Geometry and Trigonometry Explained

Welcome to SAT Geometry Essentials! Today we'll explore fundamental shapes and formulas that commonly appear on the SAT.Let's start with rectangles, one of the most common shapes you'll encounter.For rectangles, remember that area equals width times height, and perimeter equals two times the sum of width and height.Now, let's examine two special triangles that frequently appear on the SAT: the thirty-sixty-ninety triangle and the forty-five-forty-five-ninety triangle.In a thirty-sixty-ninety triangle, if the shortest side is x, then the hypotenuse is two x, and the remaining side is x times the square root of three.For the forty-five-forty-five-ninety triangle, both legs are equal, and the hypotenuse is the leg length times the square root of two.Circles are another crucial shape to understand. Remember that radius is the key measurement for both area and circumference.The area of a circle is pi r squared, and the circumference is two pi r.Let's solve a typical SAT geometry problem using what we've learned.Let's solve this step by step using our knowledge of special triangles.On the coordinate plane, we can precisely locate points and analyze geometric relationships.Let's start by understanding slope. The slope of a line measures its steepness and is calculated as rise over run.The distance formula allows us to find the length between any two points on the coordinate plane.The midpoint formula helps us find the point exactly halfway between two points.Now let's explore transformations. First, let's look at translations, which slide shapes without changing their size or shape.Reflections create mirror images of shapes across a line of reflection.Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.In right triangles, trigonometric ratios help us find unknown sides and angles.The three main trigonometric ratios are sine, cosine, and tangent.The unit circle helps us understand how trigonometric functions behave. It has a radius of 1 unit.Let's look at some important angles and their values on the unit circle.Here are the common angle values you'll need to know for the SAT.Let's solve a real SAT-style problem using trigonometry.We can use tangent to find the height. Tangent of thirty-five degrees equals the height divided by twenty meters.Rearranging the equation, we multiply twenty by tangent of thirty-five degrees.The tangent of thirty-five degrees is approximately zero point seven.Therefore, the building is fourteen meters tall.Let's review the key points for mastering trigonometry on the SAT.Good luck on your SAT! Remember these concepts and you'll be well prepared for the trigonometry questions.