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Intro to Trigonometric Ratios (SOH CAH TOA)

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Intro to Trigonometric Ratios (SOH CAH TOA) 1

Intro 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)
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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: $AC$

Question 2 of 5

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)

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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

$(i) sin theta=5/13$

$(ii) cos theta=12/13$

$(iii) tan theta=5/12$

Question 3 of 5

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)

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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.

$\color{#004ec4}{\text{opposite}=15}$

$\color{#00880a}{\text{adjacent}=8}$

$\color{#e85e00}{\text{hypotenuse}=17}$

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

$(i) sin theta=15/17$

$(ii) cos theta=8/17$

$(iii) tan theta=15/8$

Question 4 of 5

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)

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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.

$\color{#004ec4}{\text{opposite}=60}$

$\color{#00880a}{\text{adjacent}=11}$

$\color{#e85e00}{\text{hypotenuse}=61}$

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

$(i) sin theta=60/61$

$(ii) cos theta=11/61$

$(iii) tan theta=60/11$

Question 5 of 5

5. Question
Find which angle in this triangle, $A$ , $B$ or $C$ , has the following trigonometric ratios:
- $(i) tan theta=5/12:$ (A, a)
  
  $(ii) sin theta=12/13:$ (B, b)
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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.

$\tan\theta=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}=\frac{\color{#004ec4}{5}}{\color{#00880a}{12}}$

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 $B$

$(i) tantheta=5/12:A$

$(ii) sintheta=12/13:B$