Pythagorean theorem and special right triangles

If one of the corner angles is a right angle, the triangle is a spherical right triangle. A spherical triangleВ is any 3-sided region enclosed by sides that are arcs of great circles. A great circleВ on a sphere is any circle whose center coincides with the center of the sphere. The total area of the trapezoid = 360+210 = 570, or (D).Did you know there is a version of theВ Pythagorean TheoremВ for right triangles on spheres?ДЇirst, letвЂ™s define precisely what we mean by a spherical triangle. Find the area of each shape and then add them together to find the area of the trapezoid.ДЄrea of rectangle = length x width. Draw a line from point A across this figure to form the two shapes. The trapezoid consists of two smaller shapes: a triangle and a rectangle. What is the area of the trapezoidВ in the figure provided? Out of the remaining choices, only (C) correctly expresses the ratio. We know the ratio for a 45-45-90 isВ x: x: xв€љ2, which means two of the sides must be equal. The answer is (E).ДЄВ fractional exponent is just another way of expressing a root. If triangle ABC is a 30-60-90 right triangle, which of the following sets could represent triangle ABCвЂ™s side lengths?ДЇor each answer choice x = 2, so knowing that the ratio of a 30-60-90 isВ x: xв€љ3 : 2x, you can plug x in to get: 2: 2в€љ3 : 2(2) or 2: 2в€љ3 : 4. If 2в€љ3 is across from the 60-degree angle, then x = 2. A 30-60-90 triangle has a ratio of x: xв€љ3: 2x. It is a good example of how drawing the triangle can be vital to getting the correct answer on a right triangle question.

If side 2в€љ3 is across from the 60-degree angle, what is the measurement of x? The correct answer is (C).ДЄ right triangle with one length of 60 degrees has two leg lengths of x of and 2в€љ3. This means that the triangle is isosceles, and the correct answer choice must contain two equal values. So, (A) and (B) are eliminated.В To choose between (C), (D), and (E), notice that a right triangle with one 45 degree angle must have another 45 degree angle. Here, even if you forgot the 45-45-90 ratios, you can eliminate any choice that doesnвЂ™t meet the Pythagorean theorem, since the question tells you are dealing with a right triangle. Which of the following sets of three numbers could be the side lengths, in yards, of a right triangle containing a 45В° angle? Its sides will always be in a ratio ofВ x: x: xв€љ2. Its sides will always be in a ratio ofВ x: xв€љ3 : 2x.В The other special triangle is the 45-45-90В triangle. There are also two right triangles that are very important to know called the special right triangles.В These are so called because the ratio of their sides never changes. This looks like 3:4:5, so x/2 = 4, and x = 8. ThatвЂ™s because it must fit a 6:x:10 ratio, which if we divide by two becomes 3:(x/2):5. These ratios are also true for any multiples of 3:4:5 and 5:12:13 such as 6:8:10 or 10:24:26.ДЇor example, if you are told a right triangle has a hypotenuse of 10 and one side with a length of 6, you can tell that the third side is 8. These are common ratios between the sides that come up often in right triangles. To save time, you can memorize and recognize the common Pythagorean triplets.

Hypotenuse is the name given to the side across from the 90-degree angle. In which a and b are the two shorter sides and c is the hypotenuse. The Pythagorean Theorem can be represented as It only works for a right triangle, a triangle with a 90-degree angle. The Pythagorean Theorem is a formula used to find the third side of a right triangle if you know the other two sides. The Pythagorean Theorem and the properties of right triangles are especially tested. Out of all theВ ACT Math topicsВ tested, the triangle is the most commonly tested Geometric shape.

Pythagorean theorem and special right triangles