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Intro to Trigonometric Ratios (SOH CAH TOA) 2Intro to Trigonometric Ratios (SOH CAH TOA) 2
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Question 1 of 4
1. Question
Find which angle in this triangle, `Q`, `P` or `R`, has the following trigonometric ratios:
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`(i) cos theta=21/29:` (R, r)`(ii) tan theta=21/20:` (P, p)
Hint
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
Sin Ratio (SOH)
$$\sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio (CAH)
$$\cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio (TOA)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$Label the triangle according to each given trigonometric ratio to find the angles.$$\cos\theta=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}=\frac{\color{#00880a}{21}}{\color{#e85e00}{29}}$$
The angle adjacent to `21` and has a hypotenuse of `29` is `R`$$\tan\theta=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}=\frac{\color{#004ec4}{21}}{\color{#00880a}{20}}$$
The angle opposite of `21` and is adjacent to `20` is `P``(i) costheta=21/29:R``(ii) tantheta=21/20:P` -
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Question 2 of 4
2. Question
If `tan theta=20/21`, find the following trigonometric ratios.Write fractions in the format “a/b”-
`(i) sin theta=` (20/29)`(ii) cos theta=` (21/29)
Hint
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
Sin Ratio (SOH)
$$\sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio (CAH)
$$\cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio (TOA)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$Pythagoras’ Theorem
$$\color{#e85e00}{c}^2=\color{#004ec4}{a}^2+\color{#00880a}{b}^2$$First, draw a random right triangle and use the `tan` ratio to label it.$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}=\frac{\color{#004ec4}{20}}{\color{#00880a}{21}}$$
To find the missing side which is the hypotenuse, use Pythagoras’ Theorem.`a=20``b=21`$$\color{#e85e00}{c}^2$$ `=` $$\color{#004ec4}{a}^2+\color{#00880a}{b}^2$$ Pythagoras’ Theorem $$\color{#e85e00}{c}^2$$ `=` $$\color{#004ec4}{20}^2+\color{#00880a}{21}^2$$ Plug in the values $$\color{#e85e00}{c}^2$$ `=` `400+441` $$\color{#e85e00}{c}^2$$ `=` `841` $$\sqrt{\color{#e85e00}{c}^2}$$ `=` `sqrt841` Take the square root of both sides `c` `=` `29` 
$$\color{#004ec4}{\text{opposite}=20}$$$$\color{#00880a}{\text{adjacent}=21}$$$$\color{#e85e00}{\text{hypotenuse}=29}$$Now, solve for the other Trigonometric Ratios using the given formulas.`sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin` ratio `=` $$\frac{\color{#004ec4}{20}}{\color{#e85e00}{29}}$$ Plug in the values `cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos` ratio `=` $$\frac{\color{#00880a}{21}}{\color{#e85e00}{29}}$$ Plug in the values `(i) sin theta=20/29``(ii) cos theta=21/29` -
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Question 3 of 4
3. Question
If `sin alpha=12/13`, find the following trigonometric ratios.Write fractions in the format “a/b”-
`(i) cos alpha=` (5/13)`(ii) tan alpha=` (12/5)
Hint
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Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
Sin Ratio (SOH)
$$\sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio (CAH)
$$\cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio (TOA)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$Pythagoras’ Theorem
$$\color{#e85e00}{c}^2=\color{#004ec4}{a}^2+\color{#00880a}{b}^2$$First, draw a random right triangle and use the `sin` ratio to label it.$$\sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}=\frac{\color{#004ec4}{12}}{\color{#e85e00}{13}}$$
To find the missing side which is the adjacent, use Pythagoras’ Theorem.`a=12``c=13`$$\color{#e85e00}{c}^2$$ `=` $$\color{#004ec4}{a}^2+\color{#00880a}{b}^2$$ Pythagoras’ Theorem $$\color{#e85e00}{13}^2$$ `=` $$\color{#004ec4}{12}^2+\color{#00880a}{b}^2$$ Plug in the values `169` `=` $$144+\color{#00880a}{b}^2$$ `169``-144` `=` $$144+\color{#00880a}{b}^2\color{#CC0000}{-144}$$ Subtract `144` from both sides `25` `=` $$\color{#00880a}{b}^2$$ `sqrt25` `=` $$\sqrt{\color{#00880a}{b}^2}$$ Take the square root of both sides `5` `=` `b` `b` `=` `5` 
$$\color{#004ec4}{\text{opposite}=12}$$$$\color{#00880a}{\text{adjacent}=5}$$$$\color{#e85e00}{\text{hypotenuse}=13}$$Now, solve for the other Trigonometric Ratios using the given formulas.`cos alpha` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos` ratio `=` $$\frac{\color{#00880a}{5}}{\color{#e85e00}{13}}$$ Plug in the values `tan alpha` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan` ratio `=` $$\frac{\color{#004ec4}{12}}{\color{#00880a}{5}}$$ Plug in the values `(i) cos alpha=5/13``(ii) tan alpha=12/5` -
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Question 4 of 4
4. Question
If `tan theta=1/2`, find `x`.
- `x=` (3)
Hint
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Fantastic!
Incorrect
Trigonometric Ratios (SOHCAHTOA) for Right Angled Triangles
Sin Ratio (SOH)
$$\sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio (CAH)
$$\cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio (TOA)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First, label the given `tan theta` value.$$\tan\theta=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}=\frac{\color{#004ec4}{1}}{\color{#00880a}{2}}$$Also, find the opposite and adjacent values for the angle `theta` according to the given triangle.
$$\tan\theta=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}=\frac{\color{#004ec4}{x}}{\color{#00880a}{6}}$$Finally, equate the two `tan theta` values and solve for `x`.$$\frac{\color{#004ec4}{1}}{\color{#00880a}{2}}$$ `=` $$\frac{\color{#004ec4}{x}}{\color{#00880a}{6}}$$ `2x` `=` `6(1)` Cross multiply `2x` `=` `6` `2x``divide2` `=` `6``divide2` Divide both sides by `2` `x` `=` `3` `x=3`
Quizzes
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- Intro to Trigonometric Ratios (SOH CAH TOA) 2
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- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Law of Sines: Solving for a Side
- Law of Sines: Solving for an Angle
- Law of Cosines: Solving for a Side
- Law of Cosines: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)