#trignometry example

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TRIGNOMETRY RATIOS: SOHCAHTOA

In trigonometry for right triangles, the acronym of ratios SOHCAHTOA can be used to find unknown values.

SOH : sin = opposite/hypotenuse CAH : cos = adjacent/hypotenuse TOA : tan = opposite/adjacent

Before using SOHCAHTOA, it’s important to establish the hypotenuse, opposite and adjacent.

Opposite, hypotenuse, adjacent? What?

The hypotenuse is the longest side in a right triangle. The opposite and adjacent sides of a triangle will change, depending on the angle.

For example:

In regards to angle x, the side that is opposite is facing the angle - labeled in purple. The side that is adjacent is next to the angle - labeled in orange.

In regards to angle y, the side that is opposite is facing the angle - labeled in purple. The side that is adjacent is next to the angle - labeled in orange.

Using SOHCAHTOA

SOH : sin = opposite/hypotenuse CAH : cos = adjacent/hypotenuse TOA : tan = opposite/adjacent

SOHCAHTOA is used to find missing sides, and inverse SOHCAHTOA is used to find missing angles.

For example:

In regards to angle θ, sinθ = 3/5, cosθ = 4/5, and tanθ = 3/4.

INVERSE SOHCAHTOA

Inverse SOHCAHTOA uses the same two sides of a triangle as SOHCAHTOA does, but this time in order to solve for the measure of an angle.

Inverse SOH: sin⁻¹ (opposite/hypotenuse) = angle θ Inverse CAH: cos⁻¹ (adjacent/hypotenuse) = angle θ Inverse TOA: tan⁻¹ (opposite/adjacent) = angle θ

For example:

In regards of angle θ, sin⁻¹ = 8/10, cos⁻¹ = 6/10, tan⁻¹ = 8/6.

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CBSE Class 11 Courses Module

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