SOHCAHTOA calculator

A SOHCAHTOA calculator finds a missing side or angle of a right triangle using sine, cosine or tangent. SOH CAH TOA is the memory aid for the three ratios: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. Our Trigonometry Calculator does this two ways: it solves the whole triangle from two values, or it works out a single sum such as 12 sin(28) in its Evaluate box.

Both ways are in the same calculator. Solving the triangle gives every side and angle at once. The Evaluate box is quicker when you have already chosen the ratio and just need the number.

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Trigonometry Calculator

Interactive triangle solver with step-by-step

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How to use the calculator for SOHCAHTOA

Way 1: solve the whole right triangle

1. Open the calculator and choose Standard triangle at the top of the sidebar. It starts on the unit circle.
2. Under Triangle, in the panel "Type any three values, including a side, then Solve", press Right angle at C.
3. Put your angle in the A box. Then, seen from angle A, side a is the opposite, side b is the adjacent and side c is the hypotenuse.
4. Type the side you know in its box and press Solve. To find an angle instead, type two sides and leave A empty.

Measurements then lists every side and angle. The Formulas section shows SOH, CAH and TOA cards with your triangle's numbers in, such as sin = opp/hyp with the actual lengths. The calculator gives the answers but does not write out the working for a solve.

Way 2: one sum in the Evaluate box

Find the Evaluate section and type the sum. With Degrees on, which is the default, angles are read in degrees and inverse functions give degrees. Typing 12sin(28) gives 5.633659, and typing atan(5/8) gives 32.005383. The inverse functions are written asin, acos and atan.

What SOHCAHTOA means

First label the sides from the angle you are using, called θ (theta). The hypotenuse is the longest side, opposite the right angle. The opposite side is across from θ. The adjacent side is next to θ and is not the hypotenuse.

Opposite and adjacent swap if you use the other acute angle, so always label from the angle in the question.

How to choose sin, cos or tan

Look at the three sides and cross out the one you neither know nor want. The two that are left tell you the ratio.

Try picking the ratio for a triangle, then press Mark to check it in the course:

Worked examples you can check in the calculator

Example 1: opposite from the hypotenuse (SOH)

The hypotenuse is 12 and the angle is 28°. Find the side opposite the angle. Opposite and hypotenuse means sine:

Check: Right angle at C, c = 12, A = 28, Solve gives a = 5.63. Or type 12sin(28) in Evaluate.

Example 2: adjacent from the hypotenuse (CAH)

The hypotenuse is 9 and the angle is 52°. Find the adjacent side. Adjacent and hypotenuse means cosine:

In the solver, type c = 9 and A = 52: the adjacent side is b = 5.54.

Example 3: opposite from the adjacent (TOA)

The adjacent side is 7 and the angle is 64°. Find the opposite side. Opposite and adjacent means tangent:

Example 4: when the unknown is on the bottom

The opposite side is 7 and the angle is 64°. Find the hypotenuse. That is SOH again, but now the unknown is on the bottom of the fraction, so rearrange before you put numbers in:

A common slip is to multiply, giving 7 sin 64° = 6.29, which is shorter than the opposite side and so cannot be a hypotenuse. In the solver, type a = 7 and A = 64: c = 7.79.

Example 5: finding an angle

The opposite side is 5 and the adjacent side is 8. Find the angle. Opposite and adjacent means tangent, and to undo it use the inverse:

In the solver, type a = 5 and b = 8 with the right angle at C: A = 32.01°. Try finding an angle yourself:

Example 6: a ladder against a wall

A 6 m ladder leans against a wall at 72° to the ground. How high up the wall does it reach, and how far is its foot from the wall? The ladder is the hypotenuse. The height is opposite the 72° angle and the distance along the ground is adjacent to it:

One solve gives both: c = 6 and A = 72 with the right angle at C give a = 5.71 and b = 1.85.

Exact values for 30°, 45° and 60°

These angles have exact sine, cosine and tangent values, which come up in tests without a calculator.

They come from the 45-45-90 and 30-60-90 triangles, and the unit circle guide extends them to every angle. To solve a whole right triangle, including the area and perimeter, see the right triangle calculator guide.

Common mistakes

• Labelling from the wrong angle. Opposite and adjacent depend on the angle you are using. Label from that angle every time.
• Calling the hypotenuse the adjacent. The hypotenuse is next to the angle too, but it is always the side opposite the right angle.
• Multiplying when the unknown is on the bottom. If the unknown is the hypotenuse in SOH or CAH, or the adjacent in TOA, divide.
• A calculator in radians. sin 30 should be 0.5. If you get −0.988, switch to degrees.
• Pressing sin instead of sin⁻¹ for an angle. To find an angle from a ratio, use the inverse: shift or 2nd, then sin.
• Using SOH CAH TOA on a triangle with no right angle. For other triangles, use the law of sines or the law of cosines.

Practise SOHCAHTOA in a short timed paper

Right triangle trigonometry comes up in Geometry, Algebra 2 & SAT Math practice, and in GCSE Maths Higher in the UK. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. The Trigonometry course starts with labelling the sides and builds up one ratio at a time.

Read next

Maths · TrigonometrySOHCAHTOA: what it means and how to use it, with examplesWhat SOHCAHTOA stands for, how to label opposite, adjacent and hypotenuse, how to find missing sides and angles, and angle of elevation problems.