How to Find the Side Lengths of a Triangle When You Know the Angles

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 find the sides of a correct triangle
• How to find the bending of a right triangle
• How exercise yous solve a right angle triangle with only 1 side?
• How to notice the missing side of a right triangle? How to find the angle? Example
• FAQ

Finding out the missing side or angle couldn't be easier than with our swell tool - right triangle side and angle calculator. Cull ii given values, blazon them into the calculator and the remaining unknowns will be adamant in a glimmer of an eye! If you are wondering how to find the missing side of a right triangle, keep scrolling and you'll find the formulas behind our calculator.

How to find the sides of a right triangle

There are a few methods of obtaining correct triangle side lengths. Depending on what is given, you tin use different relationships or laws to find the missing side:

1. Given 2 sides

If yous know two other sides of the right triangle, it's the easiest selection; all you need to do is apply the Pythagorean theorem:

a² + b² = c²

• if leg a is the missing side, then transform the equation to the grade when a is on ane side, and take a foursquare root:

  a = √(c² - b²)

• if leg b is unknown, and then

  b = √(c² - a²)

• for hypotenuse c missing, the formula is

  c = √(a² + b²)

2. Given angle and hypotenuse

Employ the law of sines or trigonometry to find 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

Find the missing leg using trigonometric functions:

• a = b * tan(α)

• b = a * tan(β)

4. Given area and 1 leg

Every bit nosotros remember from basic triangle area formula, we can summate the area by multiplying triangle height and base and dividing the result by 2. A correct triangle is a special example of a scalene triangle, in which ane leg is the top when the second leg is the base, so the equation gets simplified to:

surface area = a * b / ii

For case, 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 * surface area / a
• c = √(a² + (2 * surface area / a)²)

How to notice the angle of a correct triangle

If yous know 1 angle autonomously from the right angle, calculation of the third one is a slice of cake:

Given β: α = xc - β

Given α: β = 90 - α

However, if only two sides of a triangle are given, finding the angles of a right triangle requires applying some basic trigonometric functions:

for α

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

How do you solve a right angle triangle with merely 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 go the length of the side opposite to the bending.
2. Alternatively, multiply the hypotenuse by cos(θ) to get the side adjacent to the angle.
3. If you accept the non-hypotenuse side side by side to the angle, split up it past cos(θ) to get the length of the hypotenuse.
4. Alternatively, multiply this length by tan(θ) to get the length of the side contrary to the angle.
5. If y'all take an angle and the side opposite to it, you can divide the side length by sin(θ) to get the hypotenuse.
6. Alternatively, split up the length by tan(θ) to become the length of the side adjacent to the bending.

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

Let'southward show how to observe the sides of a right triangle with this tool:

1. Assume we want to notice the missing side given expanse and ane side. Select the proper choice from a drib-down list. It'due south the third one.
2. Type in the given values. For instance, an expanse of a right triangle is equal to 28 in² and b = 9 in.
3. Our right triangle side and angle reckoner displays missing sides and angles! Now we know that:

• a = 6.222 in
• c = 10.941 in
• α = 34.66°
• β = 55.34°

Now, permit'southward check how does finding angles of a right triangle work:

1. Refresh the calculator. Pick the option you demand. Assume that we have two sides and we want to find all angles. The default pick is the right one.
2. Enter the side lengths. Our right triangle has a hypotenuse equal to 13 in and a leg a = 5 in.
3. Missing side and angles appear. In our example, b = 12 in, α = 67.38° and β = 22.62°.

FAQ

How many lines of symmetry does a right triangle have?

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

Can a right angled triangle have equal sides?

No, a right triangle cannot have all 3 sides equal, equally all three angles cannot besides be equal, as one has to be ninety° by definition. A right triangle can, however, have its two not-hypotenuse sides be equal in length. This would besides mean the 2 other angles are equal to 45°.

Are all right triangles similar?

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

Hanna Pamuła , PhD candidate

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

kisercrautepred.blogspot.com

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

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