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Trig Ratios: Solving for a Side

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Trig Ratios: Solving for a Side 2

Trig Ratios: Solving for a Side 2

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Question 1 of 5

Find

$x$

Round your answer to

$2$ decimal places

$x=$ (10.49)cm

Incorrect

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Trigonometric Ratios (SOHCAHTOA)

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)

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

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

$=$

$=$ Equal function

First, label the triangle in reference to the given angle.

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

$\color{#00880a}{\text{adjacent}}=\color{#00880a}{28}$

Since we now have the opposite and adjacent values, we can use the

$tan$ ratio to find

$x$ .

$tan20°32’$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$

$tan20°32’$	$=$	$\frac{\color{#004ec4}{x}}{\color{#00880a}{28}}$

$28xx$ $tan20°32’$	$=$	$x/28$ $xx28$	Multiply both sides by $28$

$28tan20°32’$	$=$	$x$
$x$	$=$	$28tan20°32’$

Simplify this further by evaluating

$tan20°32’$ using the calculator:

$1.$ Press $tan$

$2.$ Press

$20$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$32$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.374548$

Continue solving for

$x$ .

$tan20°32’=0.374548$

$x$	$=$	$28tan20°32’$
	$=$	$28times0.374548$
	$=$	$10.48734$ cm
	$=$	$10.49$ cm	Rounded off to $2$ decimal places

$10.49$ cm

Question 2 of 5

Find

$h$

Round your answer to

$2$ decimal places

$h=$ (55.63)cm

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Trigonometric Ratios (SOHCAHTOA)

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)

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

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

$=$

$=$ Equal function

First, label the triangle in reference to the given angle.

$\color{#00880a}{\text{adjacent}}=\color{#00880a}{37.8}$

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

Since we now have the adjacent value and the hypotenuse, we can use the

$cos$ ratio to find

$h$ .

$cos47°12’$	$=$	$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$

$cos47°12’$	$=$	$\frac{\color{#00880a}{37.8}}{\color{#e85e00}{h}}$

$h$	$=$	$37.8/(cos47°12′)$	Swap the constant on the left side and the denominator on the right side

Simplify this further by evaluating

$cos47°12’$ using the calculator:

$1.$ Press $cos$

$2.$ Press

$47$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$12$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.67944$

Continue solving for

$h$ .

$cos47°12’=0.67944$

$h$	$=$	$37.8/(cos47°12′)$

	$=$	$37.8/0.67944$

	$=$	$55.63405$ cm
	$=$	$55.63$ cm	Rounded off to $2$ decimal places

$55.63$ cm

Question 3 of 5

Find

$h$

Round your answer to

$2$ decimal places

$h=$ (9.60, 9.6)cm

Incorrect

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Mute

Trigonometric Ratios (SOHCAHTOA)

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)

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

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

$=$

$=$ Equal function

First, label the triangle in reference to the given angle.

$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{9.2}$

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

Since we now have the opposite value and the hypotenuse, we can use the

$sin$ ratio to find

$h$ .

$sin73°26’$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$

$sin73°26’$	$=$	$\frac{\color{#004ec4}{9.2}}{\color{#e85e00}{h}}$

$h$	$=$	$9.2/(sin73°26′)$	Swap the constant on the left side and the denominator on the right side

Simplify this further by evaluating

$sin73°26’$ using the calculator:

$1.$ Press $sin$

$2.$ Press

$73$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$26$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.958489$

Continue solving for

$h$ .

$sin73°26’=0.958489$

$h$	$=$	$9.2/(sin73°26′)$

	$=$	$9.2/0.958489$

	$=$	$9.5984$ cm
	$=$	$9.60$ cm	Rounded off to $2$ decimal places

$9.60$ cm

Question 4 of 5

Find

$y$

Round your answer to

$2$ decimal places

$y=$ (92.72)cm

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Mute

Trigonometric Ratios (SOHCAHTOA)

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)

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

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

$=$

$=$ Equal function

First, label the triangle in reference to the given angle.

$\color{#00880a}{\text{adjacent}}=\color{#00880a}{78.4}$

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

Since we now have the adjacent value and the hypotenuse, we can use the

$cos$ ratio to find

$y$ .

$cos32°16’$	$=$	$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$

$cos32°16’$	$=$	$\frac{\color{#00880a}{78.4}}{\color{#e85e00}{y}}$

$y$	$=$	$78.4/(cos32°16′)$	Swap the constant on the left side and the denominator on the right side

Simplify this further by evaluating

$cos32°16’$ using the calculator:

$1.$ Press $cos$

$2.$ Press

$32$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$16$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.84557$

Continue solving for

$y$ .

$cos32°16’=0.84557$

$y$	$=$	$78.4/(cos32°16′)$

	$=$	$78.4/0.84557$

	$=$	$92.71852$ cm
	$=$	$92.72$ cm	Rounded off to $2$ decimal places

$92.72$ cm

Question 5 of 5

Find the following lengths:

Round your answer to

$1$ decimal place

$(i) BD=$ (17.6)cm

$(ii) BC=$ (78.2)cm

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Trigonometric Ratios (SOHCAHTOA)

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)

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

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

$=$

$=$ Equal function

$(i)$ Solving for

$BD$

First, label the triangle in reference to the given angle on the left side.

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

$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{19}$

Since we now have the opposite value and the hypotenuse, we can use the

$sin$ ratio to find

$BD$ .

$sin68°$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$

$sin68°$	$=$	$\frac{\color{#004ec4}{BD}}{\color{#e85e00}{19}}$

$sin68°$ $times19$	$=$	$(BD)/19$ $times19$	Multiply both sides by $19$

$19sin68°$	$=$	$BD$
$BD$	$=$	$19sin68°$

Simplify this further by evaluating

$sin68°$ using the calculator:

$1.$ Press $sin$

$2.$ Press

$68$ and DMS or $° ‘ ‘ ‘$

$3.$ Press $=$

The result will be:

$0.92718$

Continue solving for

$BD$ .

$sin68°=0.92718$

$BD$	$=$	$19timessin68°$
	$=$	$19times0.92718$
	$=$	$17.616$ cm
	$=$	$17.6$ cm	Rounded off to $1$ decimal place

$(ii)$ Solving for

$BC$

First, label the triangle in reference to the given angle on the right side.

$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{17.6}$

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

Since we now have the opposite value and the hypotenuse, we can use the

$sin$ ratio to find

$BC$ .

$sin13°$	$=$	$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$

$sin13°$	$=$	$\frac{\color{#00880a}{17.6}}{\color{#e85e00}{BC}}$

$BC$	$=$	$17.6/(sin13°)$	Swap the constant on the left side and the denominator on the right side

Simplify this further by evaluating

$sin13°$ using the calculator:

$1.$ Press $sin$

$2.$ Press

$13$ and DMS or $° ‘ ‘ ‘$

$3.$ Press $=$

The result will be:

$0.22495$

Continue solving for

$BC$ .

$sin13°=0.22495$

$h$	$=$	$17.6/(sin13°)$

	$=$	$17.6/0.22495$

	$=$	$78.2392$ cm
	$=$	$78.2$ cm	Rounded off to $1$ decimal place

$(i) BD=17.6$ cm

$(ii) BC=78.2$ cm