Trig Ratios: Solving for a Side 1
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Question 1 of 5
1. Question
Find `x`
Round your answer to `1` decimal place- `x=` (6.3)`cm`
Hint
Help VideoCorrect
Exceptional!
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 functionDMS or `° ‘ ‘ ‘` `=` Degree/Minute/Second`=` `=` Equal functionFirst, 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
2. Question
Find `y`
Round your answer to `1` decimal place- `y=` (33.9)cm
Hint
Help VideoCorrect
Well Done!
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 functionDMS or `° ‘ ‘ ‘` `=` Degree/Minute/Second`=` `=` Equal functionFirst, 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
3. Question
Find `a`
Round your answer to `2` decimal places- `a=` (30.98)cm
Hint
Help VideoCorrect
Fantastic!
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 functionDMS or `° ‘ ‘ ‘` `=` Degree/Minute/Second`=` `=` Equal functionFirst, 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
4. Question
Find `p`
Round your answer to `1` decimal place- `p=` (14.8)cm
Hint
Help VideoCorrect
Good Job!
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 functionDMS or `° ‘ ‘ ‘` `=` Degree/Minute/Second`=` `=` Equal functionFirst, 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
5. Question
Find `a`
Round your answer to `1` decimal place- `a=` (71.6)m
Hint
Help VideoCorrect
Excellent!
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 functionDMS or `° ‘ ‘ ‘` `=` Degree/Minute/Second`=` `=` Equal functionFirst, 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
Quizzes
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Sine Rule: Solving for a Side
- Sine Rule: Solving for an Angle
- Cosine Rule: Solving for a Side
- Cosine Rule: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)