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Intro to Trigonometric Ratios (SOH CAH TOA)>
Intro to Trigonometric Ratios (SOH CAH TOA) 1Intro to Trigonometric Ratios (SOH CAH TOA) 1
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Question 1 of 5
1. Question
Name the following sides with respect to angle `theta` in the triangle below.
The sides can either be `AB`, `AC` or `BC`.-
`(i)` Opposite: (BC, CB)`(ii)` Adjacent: (AB, BA)`(iii)` Hypotenuse: (AC, CA)
Hint
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We can easily identify the hypotenuse as it is simply the side opposite the right angle.
Therefore, the hypotenuse is side `AC`.Next, the opposite side is exactly the side opposite the angle `theta`.
Therefore, the opposite side is side `BC`.Finally, the adjacent side is exactly the side next to the angle `theta`, but not the hypotenuse.
Therefore, the adjacent side is side `AB`.`(i)` Opposite: `BC``(ii)` Adjacent: `AB``(iii)` Hypotenuse: `AC` -
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Question 2 of 5
2. Question
Find the following trigonometric ratios using the given triangle.
Write fractions in the format “a/b”-
`(i) sin theta=` (5/13)`(ii) cos theta=` (12/13)`(iii) tan theta=` (5/12)
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)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First, label the values in the triangle.
$$\color{#004ec4}{\text{opposite}=5}$$$$\color{#00880a}{\text{adjacent}=12}$$$$\color{#e85e00}{\text{hypotenuse}=13}$$Now, solve each Trigonometric Ratio using the given formulas.`sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin` ratio `=` $$\frac{\color{#004ec4}{5}}{\color{#e85e00}{13}}$$ Plug in the values `cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos` ratio `=` $$\frac{\color{#00880a}{12}}{\color{#e85e00}{13}}$$ Plug in the values `tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan` ratio `=` $$\frac{\color{#004ec4}{5}}{\color{#00880a}{12}}$$ Plug in the values `(i) sin theta=5/13``(ii) cos theta=12/13``(iii) tan theta=5/12` -
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Question 3 of 5
3. Question
Find the following trigonometric ratios using the given triangle.
Write fractions in the format “a/b”-
`(i) sin theta=` (15/17)`(ii) cos theta=` (8/17)`(iii) tan theta=` (15/8)
Hint
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Well Done!
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 values in the triangle.
$$\color{#004ec4}{\text{opposite}=15}$$$$\color{#00880a}{\text{adjacent}=8}$$$$\color{#e85e00}{\text{hypotenuse}=17}$$Now, solve each Trigonometric Ratio using the given formulas.`sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin` ratio `=` $$\frac{\color{#004ec4}{15}}{\color{#e85e00}{17}}$$ Plug in the values `cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos` ratio `=` $$\frac{\color{#00880a}{8}}{\color{#e85e00}{17}}$$ Plug in the values `tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan` ratio `=` $$\frac{\color{#004ec4}{15}}{\color{#00880a}{8}}$$ Plug in the values `(i) sin theta=15/17``(ii) cos theta=8/17``(iii) tan theta=15/8` -
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Question 4 of 5
4. Question
Find the following trigonometric ratios using the given triangle.
Write fractions in the format “a/b”-
`(i) sin theta=` (60/61)`(ii) cos theta=` (11/61)`(iii) tan theta=` (60/11)
Hint
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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)
$$\tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First, label the values in the triangle.
$$\color{#004ec4}{\text{opposite}=60}$$$$\color{#00880a}{\text{adjacent}=11}$$$$\color{#e85e00}{\text{hypotenuse}=61}$$Now, solve each Trigonometric Ratio using the given formulas.`sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin` ratio `=` $$\frac{\color{#004ec4}{60}}{\color{#e85e00}{61}}$$ Plug in the values `cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos` ratio `=` $$\frac{\color{#00880a}{11}}{\color{#e85e00}{61}}$$ Plug in the values `tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan` ratio `=` $$\frac{\color{#004ec4}{60}}{\color{#00880a}{11}}$$ Plug in the values `(i) sin theta=60/61``(ii) cos theta=11/61``(iii) tan theta=60/11` -
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Question 5 of 5
5. Question
Find which angle in this triangle, `A`, `B` or `C`, has the following trigonometric ratios:
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`(i) tan theta=5/12:` (A, a)`(ii) sin theta=12/13:` (B, b)
Hint
Help VideoCorrect
Good Job!
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.$$\tan\theta=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}=\frac{\color{#004ec4}{5}}{\color{#00880a}{12}}$$
The angle opposite of `5` and adjacent to `12` is `A`$$\sin\theta=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}=\frac{\color{#004ec4}{12}}{\color{#e85e00}{13}}$$
The angle opposite of `12` and has a hypotenuse of `13` is `B``(i) tantheta=5/12:A``(ii) sintheta=12/13:B` -
Quizzes
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- 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
- 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)