Easy SOH CAH TOA: Right Triangle Calculator & Worksheet Fun!

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Shaz

12/02/2023

Maths

SOHCAHTOA Poster GCSE Maths

Subjects

Maths

Geometry and measure

Circle theorems - higher

Easy SOH CAH TOA: Right Triangle Calculator & Worksheet Fun!

SOHCAHTOA is a powerful trigonometric tool for solving right-angled triangle problems. It helps find missing angles and sides using sine, cosine, and tangent ratios. This guide explains how to use SOHCAHTOA for various calculations in right-angled triangles.

SOHCAHTOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent
It's used to find missing angles and lengths in right-angled triangles
The process involves identifying given sides/angles, choosing the appropriate trigonometric ratio, and solving the equation
Inverse trigonometric functions are used to find missing angles

12/02/2023

SOH CAH TOA
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H= 0 ÷Sin
Sine = 0÷H
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SC
Finding Missing Lengths.
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10 Label the
H
A
cos*H
0
64°
A = COSOXH
H = A

Finding Missing Angles Using SOHCAHTOA

This page focuses on using SOHCAHTOA to find missing angles in right-angled triangles. It explains the process of using inverse trigonometric functions to calculate unknown angles.

The steps for finding missing angles are:

Label the given lengths as O, A, or H
Determine which trigonometric ratio to use based on the given information
Set up the equation using the appropriate ratio
Use the inverse trigonometric function to solve for the angle

Highlight: To find an angle, we use inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹.

The page provides examples for each trigonometric ratio:

Using sine: Example: If O = 8.4 and H = 10.8, then θ = sin⁻¹ $8.4 ÷ 10.8$ ≈ 51.1° $3 sf$
Using cosine: Example: If A = 12 and H = 14.19, then θ = cos⁻¹ $12 ÷ 14.19$ ≈ 32.3° $3 sf$
Using tangent: Example: If O = 11.2 and A = 7.8, then θ = tan⁻¹ $11.2 ÷ 7.8$ ≈ 55.1° $3 sf$

Vocabulary: Inverse trigonometric functions $also called arcfunctions$ :

sin⁻¹ or arcsin

cos⁻¹ or arccos

tan⁻¹ or arctan

The page also provides guidance on using a calculator for these inverse functions, typically accessed through the 'shift' or 'inverse' button followed by the regular trigonometric function key.

Highlight: Always remember to use the appropriate units $degrees or radians$ and round your answers to a suitable number of significant figures or decimal places as required by the question.

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Subjects

Maths

Geometry and measure

Circle theorems - higher

Maths

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Easy SOH CAH TOA: Right Triangle Calculator & Worksheet Fun!

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Finding Missing Angles Using SOHCAHTOA

This page focuses on using SOHCAHTOA to find missing angles in right-angled triangles. It explains the process of using inverse trigonometric functions to calculate unknown angles.

The steps for finding missing angles are:

Label the given lengths as O, A, or H
Determine which trigonometric ratio to use based on the given information
Set up the equation using the appropriate ratio
Use the inverse trigonometric function to solve for the angle

Highlight: To find an angle, we use inverse trigonometric functions: sin⁻¹, cos⁻¹, or tan⁻¹.

The page provides examples for each trigonometric ratio:

Using sine: Example: If O = 8.4 and H = 10.8, then θ = sin⁻¹ $8.4 ÷ 10.8$ ≈ 51.1° $3 sf$
Using cosine: Example: If A = 12 and H = 14.19, then θ = cos⁻¹ $12 ÷ 14.19$ ≈ 32.3° $3 sf$
Using tangent: Example: If O = 11.2 and A = 7.8, then θ = tan⁻¹ $11.2 ÷ 7.8$ ≈ 55.1° $3 sf$

Vocabulary: Inverse trigonometric functions $also called arcfunctions$ :

sin⁻¹ or arcsin

cos⁻¹ or arccos

tan⁻¹ or arctan

The page also provides guidance on using a calculator for these inverse functions, typically accessed through the 'shift' or 'inverse' button followed by the regular trigonometric function key.

Highlight: Always remember to use the appropriate units $degrees or radians$ and round your answers to a suitable number of significant figures or decimal places as required by the question.

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SOH CAH TOA: Finding Missing Lengths and Angles

This page introduces the fundamental concept of SOHCAHTOA and its application in solving right-angled triangle problems. It covers the basics of finding missing lengths using trigonometric ratios.

Definition: SOHCAHTOA is a mnemonic device used to remember the ratios in trigonometry for sine, cosine, and tangent.

The page explains how to label the sides of a right-angled triangle:

Opposite $O$ : The side opposite to the angle in question
Adjacent $A$ : The side next to the angle in question
Hypotenuse $H$ : The longest side, always opposite the right angle

Highlight: The hypotenuse is always the diagonal and opposite the right angle.

To find missing lengths, the process involves:

Labeling the given side and the side you need to find $O, A, or H$
Choosing the appropriate trigonometric ratio $sine, cosine, or tangent$
Applying the formula and solving for the unknown side

Example: To find H when O and the angle are given, use H = O ÷ sin θ. For instance, if O = 10.2 and θ = 64°, then H = 10.2 ÷ sin $64$ ≈ 11.3 cm $3 sf$ .

The page also provides examples for finding the adjacent side using cosine and the opposite side using tangent.

Vocabulary:

SOH: Sine = Opposite ÷ Hypotenuse

CAH: Cosine = Adjacent ÷ Hypotenuse

TOA: Tangent = Opposite ÷ Adjacent

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Easy SOH CAH TOA: Right Triangle Calculator & Worksheet Fun!

Finding Missing Angles Using SOHCAHTOA

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Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

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Still not convinced? See what other students are saying...

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The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Easy SOH CAH TOA: Right Triangle Calculator & Worksheet Fun!

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Finding Missing Angles Using SOHCAHTOA

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SOH CAH TOA: Finding Missing Lengths and Angles

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