Solve the right triangle shown in the figure calculator

Right Triangle Shape

K = area
P = perimeter

See Diagram Below:
ha = altitude of a
hb = altitude of b
hc = altitude of c

*Length units are for your reference only since the value of the resulting lengths will always be the same no matter what the units are.

Calculator Use

A right triangle is a special case of a triangle where 1 angle is equal to 90 degrees. In the case of a right triangle a2 + b2 = c2. This formula is known as the Pythagorean Theorem.

In our calculations for a right triangle we only consider 2 known sides to calculate the other 7 unknowns. For example, if we know a and b we can calculate c using the Pythagorean Theorem. c = √(a2 + b2). Once we know sides a, b, and c we can calculate the perimeter = P, the semiperimeter = s, the area = K, and the altitudes: ha, hb, and hc. Let us know if you have any other suggestions!

Formulas and Calculations for a right triangle:

• Pythagorean Theorem for Right Triangle: a2 + b2 = c2
• Perimeter of Right Triangle: P = a + b + c
• Semiperimeter of Right Triangle: s = (a + b + c) / 2
• Area of Right Triangle: K = (a * b) / 2
• Altitude a of Right Triangle: ha = b
• Altitude b of Right Triangle: hb = a
• Altitude c of Right Triangle: hc = (a * b) / c

1. Given sides a and b find side c and the perimeter, semiperimeter, area and altitudes

• a and b are known; find c, P, s, K, ha, hb, and hc
• c = √(a2 + b2)
• P = a + b + c
• s = (a + b + c) / 2
• K = (a * b) / 2
• ha = b
• hb = a
• hc = (a * b) / c

2. Given sides a and c find side b and the perimeter, semiperimeter, area and altitudes

• a and c are known; find b, P, s, K, ha, hb, and hc
• b = √(c2 - a2)
• P = a + b + c
• s = (a + b + c) / 2
• K = (a * b) / 2
• ha = b
• hb = a
• hc = (a * b) / c

For more information on right triangles see:

Weisstein, Eric W. "Right Triangle." From MathWorld--A Wolfram Web Resource. Right Triangle.

Weisstein, Eric W. "Altitude." From MathWorld--A Wolfram Web Resource. Altitude.

Additional Information
The usual way of identifying a triangle is by first putting a capital letter on each vertex (or corner). Like, for example, A B C.
Now, a reference to A can mean either that vertex or, the size of the angle at that vertex. Here it means the size.
The edges are identified by using the small version of the opposite vertex-letter. So, a is opposite A;    b is opposite B;    c is opposite C.
Again, the small letter could be identifying the edge or the length of the edge. Here it is the length.
The name hypotenuse is given to the longest edge in a right-angled triangle. (It is the edge opposite to the right angle and is c in this case.)


Where (for brevity) it says 'edge a', 'angle B' and so on, it should, more correctly, be something like 'length of edge a' or 'edge-length' or 'size of angle B' etc.
If the perimeter is needed, add together the lengths of
edge a + edge b + edge c 

Note that giving the sizes of the two angles, A & B will not allow any other sizes to be found. At least one dimension, of edge-length or area, has to be supplied.
Remember the drawing is NOT to scale. It is for illustration of the parts only.
Sometimes two different solutions are possible. If one edge is known, and one angle; try putting in the edge length first as a and second as b; while putting in the angle as the SAME letter each time.

Our online tools will provide quick answers to your calculation and conversion needs. On this page, you can solve math problems involving right triangles. You can calculate angle, side (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height and distances.

Download: Use this right-triangle solver offline with our all-in-one calculator app for Android and iOS.

Right triangle calculation

Formulas used for calculations on this page:

Pythagoras' Theorem
a2 + b2 = c2

Trigonometric functions:
sin(A) = a/c, cos(A) = b/c, tan(A) = a/b
sin(B) = b/c, cos(B) = a/c, tan(B) = b/a

Area = a*b/2, where a is height and b is base of the right triangle.

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