Intro 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:
- $(i) cos theta=21/29:$ (R, r)
  
  $(ii) tan theta=21/20:$ (P, p)
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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 $P$

$(i) costheta=21/29:R$

$(ii) tantheta=21/20:P$

Question 2 of 4

$tan theta=20/21$ , find the following trigonometric ratios.

Write fractions in the format “a/b”

$(i) sin theta=$ (20/29)

$(ii) cos theta=$ (21/29)

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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

$(i) sin theta=20/29$

$(ii) cos theta=21/29$

Question 3 of 4

$sin alpha=12/13$ , find the following trigonometric ratios.