Soh Cah Toa Calculator

Must be strictly between 0 and 90 degrees.
Applies to the angles you type in and to the angleA / angleB / angleC outputs.
Leg a
5
Right Triangle Calculator
Leg b
8.660254
Hypotenuse c
10
Angle A
30
Angle B
60
Angle C (right angle)
90
Angle A in degrees
30 deg
Angle A in radians
0.523599 rad
Angle B in degrees
60 deg
Angle B in radians
1.047198 rad
Area
21.650635
Perimeter
23.660254
Altitude to the hypotenuse
4.330127
Hypotenuse segment next to leg a
2.5
Hypotenuse segment next to leg b
7.5
Inradius
1.830127
Circumradius
5
Median to the hypotenuse
5
sin A (opposite / hypotenuse)
0.5
cos A (adjacent / hypotenuse)
0.866025
tan A (opposite / adjacent)
0.57735
Whole-number (Pythagorean) triple
No
Solved from
hypotenuse and angle A
Worked out from Euclid, Elements, Book I Proposition 47 (the Pythagorean theorem) and 3 other sources.

How this is worked out

8 steps
  1. SOH: sin A = opposite / hypotenuse = a/c = 4.999999999999999/10 = 0.4999999999999999.
  2. CAH: cos A = adjacent / hypotenuse = b/c = 8.660254037844387/10 = 0.8660254037844387.
  3. TOA: tan A = opposite / adjacent = a/b = 4.999999999999999/8.660254037844387 = 0.5773502691896256.
  4. Solved from hypotenuse and angle A.
  5. Legs a = 4.999999999999999, b = 8.660254037844387; hypotenuse c = sqrt(a^2 + b^2) = 10.
  6. Angle A = arctan(a/b) = 29.99999999999999 deg, angle B = 90 - A = 60.00000000000001 deg.
  7. Area = a*b/2 = 21.650635094610966; perimeter = a + b + c = 23.660254037844386.
  8. Altitude to the hypotenuse = a*b/c = 4.330127018922193; the right angle's vertex projects onto the hypotenuse dividing it into a^2/c and b^2/c.

Results are general information, not financial, tax, legal, medical or engineering advice.