30 60 90 and 45 45 90 Triangle Calculator

September 28, 2023 by GEGCalculators

Hypotenuse: ${sideLength * 2}

Shorter Leg: ${sideLength}

Longer Leg: ${Math.sqrt(3) * sideLength}

For a 45-45-90 triangle:

Hypotenuse: ${sideLength * Math.sqrt(2)}

Leg: ${sideLength}

`; document.getElementById('result').innerHTML = result; } else { alert('Please enter a valid number for the side length.'); } }

Triangle Type	Angle Measures	Side Length Ratios
30-60-90	30°, 60°, 90°	1 : √3 : 2
45-45-90	45°, 45°, 90°	1 : 1 : √2

FAQs

How do you solve a 45 45 90 and 30 60 90 triangle? To solve a 45-45-90 triangle, you can use the Pythagorean theorem and the properties of isosceles right triangles. For a 30-60-90 triangle, you can use trigonometric ratios or special relationships between the sides.

How do you find the missing side of a 30 60 90 triangle? In a 30-60-90 triangle, if you know the length of one side (often the shorter leg), you can find the other sides using ratios. The longer leg is typically twice the length of the shorter leg, and the hypotenuse is the square root of 3 times the length of the shorter leg.

What is the formula for the 90 triangle? There is no specific “formula” for a 90-degree triangle, but you can use the Pythagorean theorem to relate the lengths of the sides: a^2 + b^2 = c^2, where ‘a’ and ‘b’ are the legs, and ‘c’ is the hypotenuse.

How do you find the missing side of a 45 45 90 triangle? In a 45-45-90 triangle, if you know the length of one side, you can find the other sides because both legs are congruent. You can use the Pythagorean theorem or simply multiply the known side length by the square root of 2 to find the other sides.

How do you find the missing side of a triangle? To find the missing side of a triangle, you’ll generally use the Pythagorean theorem for right triangles or the law of cosines for non-right triangles, depending on the given information.

What is the formula for the special triangles? The formula for special triangles (45-45-90 and 30-60-90) involves ratios of side lengths. For a 45-45-90 triangle, if one leg is ‘a’, then both legs are ‘a’, and the hypotenuse is ‘a√2’. For a 30-60-90 triangle, if the shorter leg is ‘a’, then the longer leg is ‘2a’, and the hypotenuse is ‘a√3’.

How do you find a side of a triangle when given an angle and a side? To find a side of a triangle when given an angle and a side length, you can use trigonometric ratios like sine, cosine, or tangent, depending on the information provided.

How to find the missing side of a triangle without a calculator? You can find the missing side of a triangle using basic geometric principles and the Pythagorean theorem or trigonometric ratios. For example, with a ruler, protractor, and compass, you can construct and measure the triangle’s sides and angles.

What’s the 30 60 90 formula? The formula for a 30-60-90 triangle involves the ratios of side lengths. If the shorter leg is ‘a’, the longer leg is ‘2a’, and the hypotenuse is ‘a√3’.

How do you find the third side of a 90-degree triangle? To find the third side of a 90-degree triangle, you can use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse: a^2 + b^2 = c^2, where ‘a’ and ‘b’ are the legs, and ‘c’ is the hypotenuse.

Why is 3 4 5 a right triangle? The triangle with side lengths 3, 4, and 5 is a right triangle because it satisfies the Pythagorean theorem: 3^2 + 4^2 = 5^2 (9 + 16 = 25). The sum of the squares of the two shorter sides equals the square of the longest side, confirming it’s a right triangle.

How do you find the missing length of a 90-degree triangle? You can find the missing length of a 90-degree triangle using the Pythagorean theorem: a^2 + b^2 = c^2, where ‘a’ and ‘b’ are the two shorter sides (legs), and ‘c’ is the hypotenuse.

How do I find the third side of a triangle? To find the third side of a triangle, you need information about the lengths of the other two sides and the angles between them. You can use the Law of Cosines for non-right triangles or the Pythagorean theorem for right triangles.

What is the rule of a triangle? There isn’t a single “rule” for triangles, but there are various principles and theorems that govern their properties and relationships between sides and angles.

What makes 45 45 90 and 30 60 90 triangles special when solving for missing sides? These triangles are special because their angles and side ratios are consistent, making them easy to work with. In a 45-45-90 triangle, the legs are congruent, and in a 30-60-90 triangle, the angles and side ratios have a clear pattern.

What are the three formulas of triangle? There isn’t a specific set of “three formulas” for triangles, but common formulas include the Pythagorean theorem, the Law of Sines, and the Law of Cosines, depending on the given information and the type of triangle.

What is the 2 3 rule in triangles? The “2:3 rule” likely refers to the ratios of side lengths in a 30-60-90 triangle. If the shorter leg is ‘a’, the longer leg is ‘2a’, and the hypotenuse is ‘a√3’.

What are the two formulas for a triangle? Two common formulas for triangles are the Pythagorean theorem (a^2 + b^2 = c^2) for right triangles and the Law of Cosines (c^2 = a^2 + b^2 – 2ab * cos(C)) for non-right triangles.

What is the rule of the side lengths of a triangle? The rule of side lengths in a triangle depends on the type of triangle. For a right triangle, it follows the Pythagorean theorem. In general, the sum of the lengths of any two sides must be greater than the length of the third side.

What is the rule for the side length of a right triangle? The rule for the side length of a right triangle is the Pythagorean theorem: a^2 + b^2 = c^2, where ‘a’ and ‘b’ are the lengths of the legs, and ‘c’ is the length of the hypotenuse.

Can you solve a triangle with no sides? You cannot solve a triangle with no side lengths or angle measures because you need at least some of this information to determine the triangle’s properties and dimensions.

What is a 30 60 90 triangle math? A 30-60-90 triangle is a right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees. The side lengths in such a triangle follow specific ratios: the shorter leg is half the length of the hypotenuse, and the longer leg is (√3)/2 times the length of the hypotenuse.

How do you find the angle of a triangle? To find an angle of a triangle, you can use trigonometric ratios (sine, cosine, tangent) or the Law of Cosines, depending on the given information.

How to find the height of a triangle? To find the height of a triangle, you can use the formula: Area = (1/2) * base * height. Solve for the height by rearranging the formula: height = (2 * Area) / base.

How to find the third side of a triangle without a right angle? To find the third side of a triangle without a right angle, you can use the Law of Cosines: c^2 = a^2 + b^2 – 2ab * cos(C), where ‘a’ and ‘b’ are the sides, ‘c’ is the third side, and ‘C’ is the angle opposite side ‘c’.

How do I find the 3rd side in a right angle triangle? In a right triangle, you can find the third side (the hypotenuse) using the Pythagorean theorem: c^2 = a^2 + b^2, where ‘a’ and ‘b’ are the lengths of the legs, and ‘c’ is the hypotenuse.

Is 8 15 17 a right triangle? Yes, 8-15-17 is a right triangle because it satisfies the Pythagorean theorem: 8^2 + 15^2 = 17^2 (64 + 225 = 289).

Is 9 12 15 a right triangle? Yes, 9-12-15 is a right triangle because it satisfies the Pythagorean theorem: 9^2 + 12^2 = 15^2 (81 + 144 = 225).

Does 6 8 10 make a right triangle? Yes, 6-8-10 is a right triangle because it satisfies the Pythagorean theorem: 6^2 + 8^2 = 10^2 (36 + 64 = 100).

Is 21 28 35 a right triangle? No, 21-28-35 does not form a right triangle because it does not satisfy the Pythagorean theorem: 21^2 + 28^2 ≠ 35^2 (441 + 784 ≠ 1225).

What is the formula of side into side? The formula “side into side” is not a standard mathematical formula. It depends on the context and what you’re trying to calculate.

Does 5 12 13 make a right triangle? Yes, 5-12-13 is a right triangle because it satisfies the Pythagorean theorem: 5^2 + 12^2 = 13^2 (25 + 144 = 169).

What is the 3 4 5 triangle theorem? The 3-4-5 triangle theorem states that if the sides of a triangle have lengths in the ratio 3:4:5, then the triangle is a right triangle.

Do triangles add up to 180 or 360? Triangles always add up to 180 degrees. The sum of the three interior angles of any triangle is 180 degrees. In a 360-degree context, triangles are a subset of polygons, and their angles are considered separately.

Is sine and cosine the same thing? No, sine (sin) and cosine (cos) are not the same thing. They are trigonometric functions used to relate angles to the sides of a right triangle. Sine relates the opposite side to the hypotenuse, while cosine relates the adjacent side to the hypotenuse.

How do you remember special right triangles? You can remember special right triangles (30-60-90 and 45-45-90) by memorizing the ratios of their side lengths and practicing solving problems involving these triangles.

What are the three special right triangles? The three special right triangles are the 45-45-90 triangle, the 30-60-90 triangle, and the 60-30-90 triangle. These triangles have specific angle measures and side length ratios.

What is the simple equation for a triangle? The simple equation for a triangle depends on what you want to find. Common equations include the Pythagorean theorem, the Law of Sines, and the Law of Cosines.

What is the three Pythagorean theorem formula? The three Pythagorean theorem formulas are for the three sides of a right triangle:

1. c^2 = a^2 + b^2 (for the hypotenuse ‘c’).
2. a^2 = c^2 – b^2 (for one leg ‘a’).
3. b^2 = c^2 – a^2 (for the other leg ‘b’).

Can 3 4 8 make a triangle? No, 3-4-8 cannot form a triangle because the sum of the two shorter sides (3 and 4) is less than the length of the longest side (8), violating the triangle inequality.

Can 5 7 10 make a triangle? Yes, 5-7-10 can make a triangle because the sum of the two shorter sides (5 and 7) is greater than the length of the longest side (10), satisfying the triangle inequality.

What is the triangle sum theorem? The triangle sum theorem states that the sum of the interior angles of a triangle is always 180 degrees.