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 calculator computes angles, sides (adjacent, opposite, hypotenuse), and area of any right-angled triangle for real-world applications. 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 type of triangle that has one angle measuring C=90°. In a right triangle, the side c that is opposite the C=90° angle 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 catheti. 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 C to the hypotenuse.

Examples for right triangle calculations:

• 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

Right triangles 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)?
• Vector 7
  Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
• 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?
• 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.
• Spruce height
  How tall was the spruce that was cut at an altitude of 8m above the ground, and the top landed at a distance of 15m from the heel of the tree?
• 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°?
• In football
  In football, the path that a defender must run to tackle the ball carrier is called the path of pursuit. If the ball carrier runs 40 yards to the end zone and the path of pursuit is 45 yards; how far apart were the ball carrier and defender when they star
• Right triangle
  Right triangle legs have lengths 71 dm and 919 mm. Calculate the area of this triangle.
• Missing side length
  Use the Pythagorean Theorem (a² + b²=c²) to find a unknown side length: a = 5; c = 13 ; b=?
• Catheti
  One of the catheti of the right triangle has a length of 12 cm. At what distance from the center of the hypotenuse is another cathetus?
• A baseball
  A baseball is hit over the 325 foot fence, which is 110 feet tall. How far did the ball carry on a straight line when it reached the fence?
• Triangle center
  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?
• RT triangle and height
  Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
• Six-sided polygon
  There is a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
• Ladder wall length
  A ladder leans against the wall. It touches the wall at the height of 340 cm, and its lower end is 160 cm away from the wall. How long is the ladder? Express the result to the nearest centimeter.

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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.