Right triangle calculator

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 of the C=90° angle, is the longest side of the triangle and is called the hypotenuse. The variables a, b are the lengths of the shorter sides, also called legs or arms. Variables for angles are A, B, or α (alpha) and β (beta). Variable h refers to the altitude(height) of the triangle, which is the length from the vertex C to the hypotenuse of the triangle.

Examples for right triangle calculation:

• two cathetuses 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:

• Triangle P2
  Can a triangle have two right angles?
• Height 2
  Calculate the height of the equilateral triangle with side 38.
• 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?
• Height
  Is right that in any right triangle height is less or equal half of the hypotenuse?
• Cableway
  Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
• Euclid2
  In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
• Calculate
  Calculate the length of a side of the equilateral triangle with an area of 50cm².
• Trapezoid - RR
  Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
• Double ladder
  The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
• Right triangle
  Right triangle legs has lengths 630 mm and 411 dm. Calculate the area of this triangle.
• Spruce height
  How tall was 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?
• Broken tree
  The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
• Four ropes
  TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment
• Cable car
  Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?

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Look also our friend's collection of math problems and questions:

• triangle
• area of shape
• 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 more information about triangles or more details on solving triangles.