Right triangle calculator

To calculate the properties of a right triangle when given certain information, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

If you know the length of the hypotenuse and one of the other two sides, you can use the Pythagorean theorem to find the length of the remaining side. For example, if you know the length of the hypotenuse is c and the length of one of the legs is a, you can find the length of the other leg by:

b² = c² - a²

Additionally, you can use the Pythagorean theorem to find the measure of the angles in a right triangle. You can use the inverse trigonometric functions such as arctan, arcsin, arccos to find the angles.

If you know the side lengths, you can use the trigonometric functions to find the angles:

sin α = a/c
cos α = b/c
tan α = a/b

It's important to note that the Pythagorean theorem holds true only for right triangles. If the triangle is not a right triangle, this theorem will not work.The right triangle calculators compute angles, sides (adjacent, opposite, hypotenuse), and area of any right-angled triangle and use it in the real world. Two independent properties entirely determine any right-angled triangle. The calculator provides a step-by-step explanation for each calculation.

A right triangle is a kind of triangle that has one angle that measures C=90°. In a Right triangle, the side c that is opposite the C=90° angle and is the longest side of the triangle and is called the hypotenuse. The symbols a and b are the lengths of the shorter sides, also called legs or arms. Symbols for angles are A (or α alpha) and B (or β beta). Symbol h refers to the altitude (height) of the triangle, which is the length of the perpendicular line segment drawn from the vertex of the triangle to the hypotenuse.

Examples for right triangle calculation:

• two catheti a and b
• cathetus a and hypotenuse c
• cathetus a and opposite angle A
• cathetus a and adjacent angle B
• hypotenuse c and angle A
• hypotenuse c and height h
• area T and hypotenuse c
• area T and cathetus a
• area T and angle A
• circumradius R and cathetus b
• perimeter p and hypotenuse c
• perimeter p and cathetus a
• inradius r and cathetus a
• inradius r and area T
• Medians m_a and m_b

A right triangle in word problems in mathematics:

• A triangle 10
  A triangle has vertices at (4, 5), (-3, 2), and (-2, 5). What are the coordinates of the vertices of the image after the translation (x, y) arrow-right (x + 3, y - 5)?
• Height of right RT
  The right triangle ABC has a hypotenuse c 9 cm long and a part of the hypotenuse cb = 3 cm. How long is the height of this right triangle?
• Vector 7
  Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
• Know one angle
  In a right-angled triangle, the measure of an angle is 40°. Find the measure of other angles of the triangle in degrees.
• Distance 4527
  There are two points, K and L, KL = 4 cm. Draw a line p passing through point K and having a distance of 4 cm from point L.
• Equilateral 5571
  The height in the equilateral triangle ABC measures the square root of 3 cm. What is the length of the center bar of this triangle?
• Interior 39791
  For the interior angles of a triangle, the angle β is twice as large, and the angle γ is three times larger than the angle α. Is this triangle right?
• Determine 82595
  A ladder is 7 meters long and is leaning against a wall so that its lower end is 4 meters away from the wall. Determine how high the ladder reaches
• Different points
  Mark 4 different points O, P, R. S. Mark of line OP, OR, OS. Measure the marked lines.
• Right trapezoid
  Calculate the area of a rectangular trapezoid whose perpendicular arm is 27 mm long and the bases are 33 mm and 19 mm long.
• Ladder and wall
  The ladder is 13 m long, and its lower part is 5 m away from the wall. How high does the ladder reach?
• In the 18
  In the right triangle ABC, The hypotenuse AB = 15 cm, and B = 25 degrees. How long is BC to the nearest centimeter?
• Right triangle
  Right triangle legs have lengths 71 dm and 919 mm. Calculate the area of this triangle.
• Altitude angle
  In complete winds-free weather, the balloon took off and remained standing exactly above the place from which it took off. It is 250 meters away from us. How high did the balloon fly when we saw it at an altitude angle of 25°?
• Hypotenuse 80461
  The ratios of the sides of a right triangle are 3: 4: 5. How long is the hypotenuse if the entire perimeter of the triangle is 48 cm?

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Also, take a look at our friend's collection of math problems and questions!

• triangle
• right triangle
• Heron's formula
• The Law of Sines
• The Law of Cosines
• Pythagorean theorem
• triangle inequality
• similarity of triangles
• The right triangle altitude theorem

See triangle basics on Wikipedia or more details on solving triangles.