Years
>
Year 10>
Trigonometry>
Trig Ratios: Solving for a Side>
Trig Ratios: Solving for a Side 2Trig Ratios: Solving for a Side 2
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
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)