Quiz 7-1 Pythagorean Theorem Special Right Triangles & Geometric Mean (2024)

FAQs

What is the Pythagorean theorem special right triangles? ›

The legs of a right triangle are the two shorter sides of the right triangle. Legs are adjacent to the right angle. The Pythagorean Theorem is a mathematical relationship between the sides of a right triangle, given by a2+b2=c2, where a and b are legs of the triangle and c is the hypotenuse of the triangle.

The Pythagorean Theorem is used to calculate a missing length in a right triangle . If you have a right angled triangle and you know two of the lengths, label the sides of the triangle a,b and c (c must be the hypotenuse – the longest side). Pythagorean Theorem is. a 2 + b 2 = c 2 .

A 45 45 90 triangle is isosceles. The two legs are equal. A 30 60 90 triangle has the hypotenuse 2 times as long as the short leg. Hope this helps!

The formula for the 2 types of special right triangles is expressed in the form of the ratio of the sides and can be written as follows: 30° 60° 90° triangle formula: Short leg: Long leg : Hypotenuse = x: x√3: 2x. 45° 45° 90° triangle formula: Leg : Leg: Hypotenuse = x: x: x√2.

The ratio of the leg and the hypotenuse of a 45-45-90 triangle is square root of 2. If you know the leg, multiply by the square root of 2 to find the hypotenuse. If you know the hypotenuse, divide by the square root of 2 to find the leg.

Solution: Given, side length, a = 12 units. We will use the formula for the height of equilateral triangle, h = (a√3)/2. Substituting the value of 'a', we get, h = (12√3)/2 = 6√3 = 10.39 units. Therefore, the height of the equilateral triangle is 10.39 units.

Answer: The sides of the triangle are 3√2, 3√6, and 3√8. Let us check whether the sides are of the 30-60-90 triangle. On dividing each side of the triangle by 3√2, we get 1, √3, and 2. Therefore, sides of the triangle are 3√2, 3√6, and 3√8, are in the ratio 1: √3: 2.

The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle.

SOHCAHTOA is a mnemonic device helpful for remembering what ratio goes with which function. SOH = Sine is Opposite over Hypotenuse. CAH = Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.

The side opposite the right angle in a right-angled triangle is called the hypotenuse. The other two sides of a right-angled triangle are called the legs. In addition to being located directly across from the right angle, the hypotenuse is always the longest side of a right-angled triangle.

What is Pythagoras law for right triangles? ›

Pythagoras Theorem Statement

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

Special Right Triangle Formula

The special right triangle formulas in the form of ratios can be expressed as: 30° 60° 90° triangle formula: Short leg: Long leg : Hypotenuse = x: x√3: 2x. 45° 45° 90° triangle formula: Leg : Leg: Hypotenuse = x: x: x√2.

A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long.

The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the triangle's legs is the same as the square of the length of the triangle's hypotenuse.