Trig Ratios: Solving for a Side 1

Question 1 of 5

Find

$x$

Round your answer to

$1$ decimal place

$x=$ (6.3) $cm$

Incorrect

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

Incorrect

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

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

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

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

Trig Ratios: Solving for a Side 1

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Quiz summary

Information

1. Question

Hint

Exceptional!

Trigonometric Ratios (SOHCAHTOA)

Sin Ratio (SOH)

Cos Ratio (CAH)

Tan Ratio (TOA)

Calculator Buttons to Use

2. Question

Hint

Well Done!

Trigonometric Ratios (SOHCAHTOA)

Sin Ratio (SOH)

Cos Ratio (CAH)

Tan Ratio (TOA)

Calculator Buttons to Use

3. Question

Hint

Fantastic!

Trigonometric Ratios (SOHCAHTOA)

Sin Ratio (SOH)

Cos Ratio (CAH)

Tan Ratio (TOA)

Calculator Buttons to Use

4. Question

Hint

Good Job!

Trigonometric Ratios (SOHCAHTOA)

Sin Ratio (SOH)

Cos Ratio (CAH)

Tan Ratio (TOA)

Calculator Buttons to Use

5. Question

Hint

Excellent!

Trigonometric Ratios (SOHCAHTOA)

Sin Ratio (SOH)

Cos Ratio (CAH)

Tan Ratio (TOA)

Calculator Buttons to Use

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