TAILIEUCHUNG - – THE SAT MATH SECTION – 45-45-90 Right Triangles 45° 30-60-90 Triangles In a right triangle

– THE SAT MATH SECTION – 45-45-90 Right Triangles 45° 30-60-90 Triangles In a right triangle with the other angles measuring 30° and 60°: ■ 45° A right triangle with two angles each measuring 45° is called an isosceles right triangle. In an isosceles right triangle: ■ ■ The leg opposite the 30-degree angle is half the length of the hypotenuse. (And, therefore, the hypotenuse is two times the length of the leg opposite the 30-degree angle.) The leg opposite the 60 degree angle is 3 times the length of the other leg. 60° The length of the hypotenuse is 2 multiplied by the length of one of the legs of. | THE SAT MATH SECTION 45-45-90 Right Triangles A right triangle with two angles each measuring 45 is called an isosceles right triangle. In an isosceles right triangle The length of the hypotenuse is V2 multiplied by the length of one of the legs of the triangle. V2 The length of each leg is 2 multiplied by the length of the hypotenuse. V2 x v w 5Vy x y 2 X 1 2 5V2 30-60-90 Triangles In a right triangle with the other angles measuring 30 and 60 The leg opposite the 30-degree angle is half the length of the hypotenuse. And therefore the hypotenuse is two times the length of the leg opposite the 30-degree angle. The leg opposite the 60 degree angle is V3 times the length of the other leg. Example X 2 X 7 14 and y 7V3 133 THE SAT MATH SECTION Triangle Trigonometry There are special ratios we can use with right triangles. They are based on the trigonometric functions called sine cosine and tangent. The popular mnemonic to use is Circles A circle is a closed figure in which each point of the circle is the same distance from a fixed point called the center of the circle. SOH CAH TOA For an angle 9 within a right triangle we can use these formulas Opposite sin 9 Hypotenuse Adjacent cos 9 Hypotenuse tan 9 Opposite tan 9 Adjacent To find sin 0. To find cos Q. Angles and Arcs of a Circle Central Angle To find tan 0. adjacent TRIG VALUES OF SOME COMMON ANGLES sin cos tan 1 V3 V3 30 2 2 3 45 V2 V2 1 2 2 60 V3 2 1 2 V3 Whereas it is possible to solve some right triangle questions using the knowledge of 30-60-90 and 45-4590 triangles an alternative method is to use trigonometry. For example solve for x below. Using the knowledge that cos 60 1 just substitute into the equation x so x 10. An arc is a curved section of a circle. A minor arc is smaller than a semicircle and a major arc is larger than a semicircle. A central angle of a circle is an angle that has its vertex at the center and that has sides that are radii. Central angles have the same degree measure as the arc it .

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