Sohcahtoa Calculator

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

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:

References:

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

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