How To Find The Missing Value Of A Triangle

Right Triangle Side and Angle Calculator

Created by Hanna Pamuła , PhD

Reviewed by

Bogna Szyk and Jack Bowater

Terminal updated:

November 18, 2022

Finding the missing side or angle couldn't be easier than with our keen tool – right triangle side and angle calculator. Cull 2 given values, type them into the calculator, and the calculator will determine the remaining unknowns in a blink of an eye! If you are wondering how to observe the missing side of a correct triangle, keep scrolling, and you lot'll notice the formulas behind our calculator.

How to find the sides of a right triangle

There are a few methods of obtaining right triangle side lengths. Depending on what is given, you lot can utilize different relationships or laws to observe the missing side:

1. Given two sides

If you know two other sides of the correct triangle, information technology's the easiest pick; 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 class where a is on ane 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)

🙋 Our Pythagorean theorem calculator will help yous if you have any doubts at this point.

2. Given an bending and the hypotenuse

Use the constabulary 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)

🙋 Refresh your knowledge with Omni's police force of sines calculator!

3. Given an angle and one leg

Find the missing leg using trigonometric functions:

• a = b × tan(α)

• b = a × tan(β)

4. Given the surface area and 1 leg

As nosotros recollect from basic triangle surface area formula, we can calculate the area by multiplying the triangle height and base of operations and dividing the result by two. A right triangle is a special case of a scalene triangle, in which 1 leg is the superlative when the second leg is the base, and then the equation gets simplified to:

area = a × b / 2

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

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

🙋 For this blazon of problem, see besides our surface area of a right triangle calculator.

How to find the angle of a right triangle

If you know one angle autonomously from the correct angle, the adding of the tertiary i is a slice of cake:

Given β: α = 90 - β

Given α: β = 90 - α

Yet, if but two sides of a triangle are given, finding the angles of a correct 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 and 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 so β = arccot(a / b) (inverse cotangent).

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

To solve a triangle with 1 side, you also need ane of the non-right angled angles. If not, it is incommunicable:

1. If yous have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle.

2. Alternatively, multiply the hypotenuse by cos(θ) to go the side side by side to the bending.

3. If you have the non-hypotenuse side next to the bending, divide it by cos(θ) to get the length of the hypotenuse.

4. Alternatively, multiply this length past tan(θ) to get the length of the side opposite to the angle.

5. If you have an angle and the side opposite to it, you can separate the side length by sin(θ) to get the hypotenuse.

6. Alternatively, divide the length by tan(θ) to get the length of the side side by side to the angle.

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

Allow'south show how to notice the sides of a right triangle with this tool:

1. Assume we want to find the missing side given area and i side. Select the proper option from a drop-down list. It's the third ane.

2. Type in the given values. For example, an area of a right triangle is equal to 28 in² and b = 9 in.

3. Our right triangle side and bending reckoner displays missing sides and angles! Now we know that:

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

Now, let's bank check how finding the angles of a right triangle works:

1. Refresh the calculator. Pick the option you need. Assume that we have two sides, and we want to find all angles. The default option is the correct one.

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 example, b = 12 in, α = 67.38° and β = 22.62°.

FAQ

How many lines of symmetry does a right triangle take?

If a correct triangle is isosceles (i.e., its two not-hypotenuse sides are the same length), it has i line of symmetry. Otherwise, the triangle volition have no lines of symmetry.

Tin a right angled triangle have equal sides?

No, a right triangle cannot have all 3 sides equal, as all 3 angles cannot likewise exist equal. One has to exist ninety° by definition. A right triangle can, nevertheless, have its two non-hypotenuse sides equal in length. This would besides mean the two other angles are equal to 45°.

Are all right triangles similar?

Not all right-angled triangles are like, although some can be. They are similar if all their angles are the same length, or if the ratio of two of their sides is the same.

30 threescore 90 triangle 45 45 xc triangle Area of a right triangle … 15 more

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

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