How To Find The Lengths Of A Triangle

Right Triangle Side and Angle Calculator

Created by Hanna Pamuła , PhD candidate

Reviewed past

Bogna Szyk and Jack Bowater

Last updated:

Nov 12, 2021

Table of contents:

• How to detect the sides of a correct triangle
• How to find the angle of a right triangle
• How exercise you solve a right angle triangle with just one side?
• How to find the missing side of a correct triangle? How to find the angle? Example
• FAQ

Finding out the missing side or bending couldn't be easier than with our keen tool - right triangle side and angle calculator. Cull two given values, type them into the calculator and the remaining unknowns will be determined in a blink of an middle! If you are wondering how to find the missing side of a right triangle, continue scrolling and you'll find the formulas behind our calculator.

How to find the sides of a right triangle

At that place are a few methods of obtaining right triangle side lengths. Depending on what is given, you can use different relationships or laws to detect the missing side:

1. Given two sides

If you know two other sides of the correct triangle, it'due south the easiest selection; all you lot need to do is apply the Pythagorean theorem:

a² + b² = c²

• if leg a is the missing side, then transform the equation to the class when a is on one side, and take a square root:

  a = √(c² - b²)

• if leg b is unknown, so

  b = √(c² - a²)

• for hypotenuse c missing, the formula is

  c = √(a² + b²)

2. Given angle and hypotenuse

Utilise the law of sines or trigonometry to discover the right triangle side lengths:

• a = c * sin(α) or a = c * cos(β)

• b = c * sin(β) or b = c * cos(α)

3. Given angle and one leg

Detect the missing leg using trigonometric functions:

• a = b * tan(α)

• b = a * tan(β)

4. Given area and 1 leg

Equally we remember from basic triangle area formula, we tin summate the surface area by multiplying triangle height and base and dividing the result by two. A right triangle is a special case of a scalene triangle, in which one leg is the elevation when the second leg is the base, then the equation gets simplified to:

expanse = a * b / 2

For example, if we know only the right triangle expanse and the length of the leg a, we can derive the equation for other sides:

• b = 2 * area / a
• c = √(a² + (2 * area / a)²)

How to find the angle of a right triangle

If you know one angle apart from the correct angle, calculation of the third one is a piece of cake:

Given β: α = 90 - β

Given α: β = xc - α

Notwithstanding, if only two sides of a triangle are given, finding the angles of a correct triangle requires applying some bones trigonometric functions:

for α

• sin(α) = a / c and then α = arcsin(a / c) (inverse sine)
• cos(α) = b / c and then α = arccos(b / c) (inverse cosine)
• tan(α) = a / b so α = arctan(a / b) (inverse tangent)
• cot(α) = b / a so α = arccot(b / a) (inverse cotangent)

and for β

• sin(β) = b / c so β = arcsin(b / c) (inverse sine)
• cos(β) = a / c and so β = arccos(a / c) (changed cosine)
• tan(β) = b / a so β = arctan(b / a) (inverse tangent)
• cot(β) = a / b and so β = arccot(a / b) (inverse cotangent)

How exercise you lot solve a right bending triangle with only one side?

To solve a triangle with one side, you lot also need 1 of the non-correct angled angles. If not, it is impossible:

1. If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle.
2. Alternatively, multiply the hypotenuse past cos(θ) to become the side next to the bending.
3. If y'all have the non-hypotenuse side next to the angle, divide it by cos(θ) to get the length of the hypotenuse.
4. Alternatively, multiply this length by tan(θ) to get the length of the side opposite to the angle.
5. If you have an bending and the side opposite to information technology, yous can carve up the side length past sin(θ) to get the hypotenuse.
6. Alternatively, divide the length by tan(θ) to get the length of the side adjacent to the angle.

How to find the missing side of a right triangle? How to observe the angle? Example

Let's show how to find the sides of a right triangle with this tool:

1. Assume nosotros desire to notice the missing side given expanse and one side. Select the proper selection from a drib-down list. It'southward the third one.
2. Blazon in the given values. For example, an surface area of a right triangle is equal to 28 in² and b = 9 in.
3. Our correct triangle side and angle calculator displays missing sides and angles! Now we know that:

• a = six.222 in
• c = x.941 in
• α = 34.66°
• β = 55.34°

At present, allow's bank check how does finding angles of a correct triangle piece of work:

1. Refresh the calculator. Pick the option you demand. Assume that nosotros take two sides and we desire to notice all angles. The default option is the correct ane.
2. Enter the side lengths. Our right triangle has a hypotenuse equal to thirteen in and a leg a = 5 in.
3. Missing side and angles appear. In our case, b = 12 in, α = 67.38° and β = 22.62°.

FAQ

How many lines of symmetry does a right triangle accept?

If a right triangle is isosceles (i.e., its two non-hypotenuse sides are the same length) it has i line of symmetry. Otherwise, the triangle will have no lines of symmetry.

Can a right angled triangle take equal sides?

No, a right triangle cannot accept all 3 sides equal, every bit all iii angles cannot besides be equal, equally 1 has to exist 90° by definition. A right triangle can, however, have its 2 non-hypotenuse sides be equal in length. This would also mean the two other angles are equal to 45°.

Are all right triangles similar?

Non all correct angled triangles are like, although some can be. They are like if all their angles are the aforementioned length, or if the ratio of 2 of their sides is the same.

Hanna Pamuła , PhD candidate

thirty 60 ninety triangle 45 45 90 triangle Area of a right triangle … 13 more

Source: https://www.omnicalculator.com/math/right-triangle-side-angle

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