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Trig Ratios: Solving for a Side>
Trig Ratios: Solving for a Side 2Trig Ratios: Solving for a Side 2
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Question 1 of 5
1. Question
Find `x`
Round your answer to `2` decimal places- `x=` (10.49)cm
Hint
Help VideoCorrect
Correct!
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.
$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{x}$$$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{28}$$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
2. Question
Find `h`
Round your answer to `2` decimal places- `h=` (55.63)cm
Hint
Help VideoCorrect
Great Work!
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.
$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{37.8}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{h}$$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
3. Question
Find `h`
Round your answer to `2` decimal places- `h=` (9.60, 9.6)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.
$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{9.2}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{h}$$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
4. Question
Find `y`
Round your answer to `2` decimal places- `y=` (92.72)cm
Hint
Help VideoCorrect
Correct!
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.
$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{78.4}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{y}$$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
5. Question
Find the following lengths:
Round your answer to `1` decimal place-
`(i) BD=` (17.6)cm`(ii) BC=` (78.2)cm
Hint
Help VideoCorrect
Awesome!
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 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 -
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)