Years
>
Year 10>
Trigonometry>
Intro to Trigonometric Ratios (SOH CAH TOA)>
Intro to Trigonometric Ratios (SOH CAH TOA) 2Intro to Trigonometric Ratios (SOH CAH TOA) 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
Question 1 of 4
1. Question
Find which angle in this triangle, `Q`, `P` or `R`, has the following trigonometric ratios:
-
`(i) cos theta=21/29:` (R, r)`(ii) tan theta=21/20:` (P, p)
Hint
Help VideoCorrect
Correct!
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)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$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` -
-
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
Help VideoCorrect
Excellent!
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)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$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` -
-
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
Help VideoCorrect
Great Work!
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)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$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` -
-
Question 4 of 4
4. Question
If `tan theta=1/2`, find `x`.
- `x=` (3)
Hint
Help VideoCorrect
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
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- 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
- Sine Rule: Solving for a Side
- Sine Rule: Solving for an Angle
- Cosine Rule: Solving for a Side
- Cosine Rule: 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)