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Trig Ratios: Solving for a Side

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Trig Ratios: Solving for a Side 1

Trig Ratios: Solving for a Side 1

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Question 1 of 5

Find

$x$

Round your answer to

$1$ decimal place

$x=$ (6.3) $cm$

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.

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

$\color{#00880a}{\text{adjacent}}=\color{#00880a}{32}$

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

$tan$ ratio to find

$x$ .

$tan11°12’$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$

$tan11°12’$	$=$	$\frac{\color{#004ec4}{x}}{\color{#00880a}{32}}$

$32xx$ $tan11°12’$	$=$	$x/32$ $xx32$	Multiply both sides by $32$

$32tan11°12’$	$=$	$x$
$x$	$=$	$32tan11°12’$

Simplify this further by evaluating

$tan11°12’$ using the calculator:

$1.$ Press $tan$

$2.$ Press

$11$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$12$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.198005$

Continue solving for

$x$ .

$tan11°12’=0.198005$

$x$	$=$	$32timestan11°12’$
	$=$	$32times0.198005$
	$=$	$6.33617$ cm
	$=$	$6.3$ cm	Rounded off to $1$ decimal place

$6.3$ cm

Question 2 of 5

Find

$y$

Round your answer to

$1$ decimal place

$y=$ (33.9)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.

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

$\color{#e65021}{\text{hypotenuse}}=\color{#e65021}{42}$

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

$cos$ ratio to find

$y$ .

$cos36°8’$	$=$	$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$

$cos36°8’$	$=$	$\frac{\color{#00880a}{y}}{\color{#e85e00}{42}}$

$42xx$ $cos36°8’$	$=$	$x/42$ $xx42$	Multiply both sides by $42$

$42cos36°8’$	$=$	$y$
$y$	$=$	$42cos36°8’$

Simplify this further by evaluating

$cos36°8’$ using the calculator:

$1.$ Press $cos$

$2.$ Press

$36$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$8$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.80764697$

Continue solving for

$y$ .

$cos36°8’=0.80764697$

$y$	$=$	$42cos36°8’$
	$=$	$42times0.80764697$
	$=$	$33.92117$ cm
	$=$	$33.9$ cm	Rounded off to $1$ decimal place

$33.9$ cm

Question 3 of 5

Find

$a$

Round your answer to

$2$ decimal places

$a=$ (30.98)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.

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

$\color{#e65021}{\text{hypotenuse}}=\color{#e65021}{39}$

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

$sin$ ratio to find

$a$ .

$sin52°35’$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$

$sin52°35’$	$=$	$\frac{\color{#004ec4}{a}}{\color{#e85e00}{39}}$

$39xx$ $sin52°35’$	$=$	$a/39$ $xx39$	Multiply both sides by $39$

$39sin52°35’$	$=$	$a$
$a$	$=$	$39sin52°35’$

Simplify this further by evaluating

$sin52°35’$ using the calculator:

$1.$ Press $sin$

$2.$ Press

$52$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$35$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.7942379$

Continue solving for

$a$ .

$sin52°35’=0.7942379$

$a$	$=$	$39sin52°35’$
	$=$	$39times0.7942379$
	$=$	$30.975$ cm
	$=$	$30.98$ cm	Rounded off to $2$ decimal places

$30.98$ cm

Question 4 of 5

Find

$p$

Round your answer to

$1$ decimal place

$p=$ (14.8)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.

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

$\color{#00880A}{\text{adjacent}}=\color{#00880A}{24}$

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

$tan$ ratio to find

$p$ .

$tan31°40’$	$=$	$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$

$tan31°40’$	$=$	$\frac{\color{#004ec4}{p}}{\color{#00880a}{24}}$

$24xx$ $tan31°40’$	$=$	$p/24$ $xx24$	Multiply both sides by $24$

$24tan31°40’$	$=$	$p$
$p$	$=$	$24tan31°40’$

Simplify this further by evaluating

$tan31°40’$ using the calculator:

$1.$ Press $tan$

$2.$ Press

$31$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$40$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.616809$

Continue solving for

$p$ .

$tan31°40’=0.616809$

$p$	$=$	$24tan31°40’$
	$=$	$24times0.616809$
	$=$	$14.8034$ cm
	$=$	$14.8$ cm	Rounded off to $1$ decimal place

$14.8$ cm

Question 5 of 5

Find

$a$

Round your answer to

$1$ decimal place

$a=$ (71.6)m

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.

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

$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{72.3}$

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

$cos$ ratio to find

$a$ .

$cos8°13’$	$=$	$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$

$cos8°13’$	$=$	$\frac{\color{#00880a}{a}}{\color{#e85e00}{72.3}}$

$72.3xx$ $cos8°13’$	$=$	$a/72.3$ $xx72.3$	Multiply both sides by $72.3$

$72.3cos8°13’$	$=$	$a$
$a$	$=$	$72.3cos8°13’$

Simplify this further by evaluating

$cos8°13’$ using the calculator:

$1.$ Press $cos$

$2.$ Press

$8$ and DMS or $° ‘ ‘ ‘$

$3.$ Press

$13$ and DMS or $° ‘ ‘ ‘$ again

$4.$ Press $=$

The result will be:

$0.989735$

Continue solving for

$a$ .

$cos8°13’=0.989735$

$a$	$=$	$72.3cos8°13’$
	$=$	$72.3times0.989735$
	$=$	$71.55782$ m
	$=$	$71.6$ m	Rounded off to $1$ decimal place

$71.6$ m