Sohcahtoa Calculator

Sohcahtoa Calculator

Enter the sides or angles of the right triangle, and the calculator will find the missing sides and angles.

Leg (a)

Leg (b)

Hypotenuse (c)

Angle (α)

deg ▾

Angle (β)

deg ▾

SOHCAHTOA Calculator:

This SOHCAHTOA calculator finds missing sides or angles of right triangles using SOH.CAH.TOA method and provides you with step-by-step solutions.

What is SOHCAHTOA?

SOH CAH TOA is a mnemonic way used to remember the formulas for main trigonometric ratios including sine (sin), cosine (cos), and tangent (tan).

Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent

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Here is what the terms mean:

Hypotenuse: The longest side, always opposite to the right angle
Opposite side: The side directly opposite to an acute angle
Adjacent side: The side that is connected to an acute angle and opposite

How SOHCAHTOA helps:

SOHCAHTOA helps to understand which of the trigonometric ratios (sine, cosine, or tangent) should be used for finding missing sides and angles.

SOH: (Sin (θ)) = Opposite Hypotenuse
CAH: (Cos (θ)) = Adjacent Hypotenuse
TOA: (Tan (θ)) = Opposite Adjacent

How To Easily Remember SOHCAHTOA?

It is easy to remember the sequence of Sin, Cos, and Tan. You need to try memorable phrases such as:

“Oscar Had A Heap Of Apples”

It implies to right angle trig functions as:

Sin(θ) = Oscar / Had = Opposite ÷ Hypotenuse
Cos(θ) = A / Heap = Adjacent ÷ Hypotenuse
Tan(θ) = Of / Apples = Opposite ÷ Adjacent

How To Solve Missing Sides Using SOHCAHTOA?

Follow these steps to work out the unknown sides of a right-angled triangle:

Write down the known and unknown sides of the right-angled triangle
Select the trig ratio that can be used to find the unknown values
Put the values into the chosen trigonometric ratio and isolate the unknown side
Perform the necessary calculations according to the chosen trig ratio and get the unknown values

Example:

A right triangle has a hypotenuse of 13 cm and an acute angle (α) of 30°. Determine the length of the side opposite angle α

Solution:

We are looking for the opposite side by having the hypotenuse, so use the SOH formula. Hence put the values and get to know the missing side.

Sin (30°) = Opposite 13 cm

We also know that Sin (30°) is a fixed value (0.5)

0.5 = Opposite 13 cm

Now, to find the missing opposite side, we can multiply both sides of the equation by 13 cm.

Opposite = 0.5 * 13 cm

Opposite = 6.5 cm

To save time and effort, try our trigonometry SOHCAHTOA calculator. It uses the SOHCAHTOA formulas to calculate the missing sides/angles of the right triangles.

Does Soh Cah Toa Only Work on Right Triangles?

Yes, it only works in the cases of right triangles. In non-right triangles, the side relationships(Hytoneous, Opposite, and Adjacent) do not hold. Therefore, it's not possible to apply SOCAHTOA to them.

SOHCAHTOA Measures of Popular Angles:

SOHCAHTOA Measures of Popular Angles

References:

From the source of en.wikipedia.org: Trigonometric ratios.

From the source of courses.lumenlearning.com: Right triangle trigonometry.