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Trig Ratios Word Problems: Solving for a Side>
Trig Ratios Word Problems: Solving for a SideTrig Ratios Word Problems: Solving for a Side
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Question 1 of 7
1. Question
A ship is anchored `410 m` from the base of a vertical cliff. The angle looking up to the top of the cliff is at an angle of `59°24’`. Calculate the height of the cliff (`h`) to the nearest metre.
- `h=` (693)`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 functionNotice that the scenario creates a triangle. Label it in reference to the given angle.
$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{h}$$$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{410}$$Since we now have the opposite and adjacent values, we can use the `tan` ratio to find `h`.`tan59°24’` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan59°24’` `=` $$\frac{\color{#004ec4}{h}}{\color{#00880a}{410}}$$ `410xx``tan59°24’` `=` `h/410``xx410` Multiply both sides by `410` `410tan59°24’` `=` `h` `h` `=` `410tan59°24’` Simplify this further by evaluating `tan59°24’` using the calculator:`1.` Press `tan``2.` Press `59` and DMS or `° ‘ ‘ ‘``3.` Press `24` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `1.690908`Continue solving for `h`.`tan59°24’=1.690908``h` `=` `410tan59°24’` `=` `410times1.690908` `=` `693.27` `=` `693 m` Rounded off to the nearest metre 
`693 m` -
Question 2 of 7
2. Question
A wire of length `5.2 m` is attached to the top of a flagpole. It is inclined to the ground at an angle of `68°32’`. Find the height of the flagpole (`h`) rounded off to `1` decimal place.
- `h=` (4.8)`m`
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 functionNotice that the scenario creates a triangle. Label it in reference to the given angle.
$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{h}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{5.2}$$Since we now have the opposite and hypotenuse values, we can use the `sin` ratio to find `h`.`sin68°32’` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin68°32’` `=` $$\frac{\color{#004ec4}{h}}{\color{#e85e00}{5.2}}$$ `5.2xx``sin68°32’` `=` `h/5.2``xx5.2` Multiply both sides by `5.2` `5.2sin68°32’` `=` `h` `h` `=` `5.2sin68°32’` Simplify this further by evaluating `sin68°32’` using the calculator:`1.` Press `sin``2.` Press `68` and DMS or `° ‘ ‘ ‘``3.` Press `32` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `0.9306306`Continue solving for `h`.`sin68°32’=0.9306306``h` `=` `5.2sin68°32’` `=` `5.2times0.9306306` `=` `4.839` `=` `4.8 m` Rounded off to `1` decimal place 
`4.8 m` -
Question 3 of 7
3. Question
A `9.7 m` ladder leans against a wall and makes an angle of `61°9’` with the ground. How far is the foot of the ladder from the base of the wall (`x`)? (`1` decimal place).
- `x=` (4.7)`m`
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 functionNotice that the scenario creates a triangle. Label it in reference to the given angle.
$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{x}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{9.7}$$Since we now have the adjacent and hypotenuse values, we can use the `cos` ratio to find `x`.`cos61°9’` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos61°9’` `=` $$\frac{\color{#00880a}{x}}{\color{#e85e00}{9.7}}$$ `9.7xx``cos61°9’` `=` `x/9.7``xx9.7` Multiply both sides by `9.7` `9.7cos61°9’` `=` `x` `x` `=` `9.7cos61°9’` Simplify this further by evaluating `cos61°9’` using the calculator:`1.` Press `cos``2.` Press `61` and DMS or `° ‘ ‘ ‘``3.` Press `9` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `0.482518`Continue solving for `x`.`cos61°9’=0.482518``x` `=` `9.7cos61°9’` `=` `9.7times0.482518` `=` `4.68` `=` `4.7 m` Rounded off to `1` decimal place 
`4.7 m` -
Question 4 of 7
4. Question
A building casts a shadow `40 m` long on the ground when the sun has an altitude (elevation) from the ground of `59°52’`. Calculate the height of the building (`h`) to the nearest metre.
- `h=` (69)`m`
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 functionNotice that the scenario creates a triangle. Label it in reference to the given angle.
$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{h}$$$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{40}$$Since we now have the opposite and adjacent values, we can use the `tan` ratio to find `h`.`tan59°52’` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan59°52’` `=` $$\frac{\color{#004ec4}{h}}{\color{#00880a}{40}}$$ `40xx``tan59°52’` `=` `h/40``xx40` Multiply both sides by `40` `40tan59°52’` `=` `h` `h` `=` `40tan59°52’` Simplify this further by evaluating `tan59°52’` using the calculator:`1.` Press `tan``2.` Press `59` and DMS or `° ‘ ‘ ‘``3.` Press `52` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `1.7227797`Continue solving for `h`.`tan59°52’=1.7227797``h` `=` `40tan59°52’` `=` `40times1.7227797` `=` `68.911` `=` `69 m` Rounded off to the nearest metre 
`69 m` -
Question 5 of 7
5. Question
Jacob is flying a kite. He is holding the string `1.5 m` above ground. The string is `32 m` long and makes an angle of `58°19’`. How high is the kite above ground `(h_t) ?` (`1` decimal place)
- `h_t =` (18.3)`m`
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 functionNotice that the scenario creates a triangle. Label it in reference to the given angle.Let `h` be the height of the kite from where Jacob is holding the string.
$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{h}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{32}$$Since we now have the adjacent and hypotenuse values, we can use the `cos` ratio to find `h`.`cos58°19’` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos58°19’` `=` $$\frac{\color{#00880a}{h}}{\color{#e85e00}{32}}$$ `32xx``cos58°19’` `=` `h/32``xx32` Multiply both sides by `32` `32cos58°19’` `=` `h` `h` `=` `32cos58°19’` Simplify this further by evaluating `cos58°19’` using the calculator:`1.` Press `cos``2.` Press `58` and DMS or `° ‘ ‘ ‘``3.` Press `19` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `0.525224`Continue solving for `h`.`cos58°19’=0.525224``h` `=` `32cos58°19’` `=` `32times0.525224` `=` `16.80717` Finally, solve for `h_t` or the total height of the kite above ground by adding `1.5` to `h`.`h_t` `=` `h+1.5` `=` `16.80717+1.5` Substitute `h` `=` `18.30717` `=` `18.3 m` Rounded off to `1` decimal place 
`18.3 m` -
Question 6 of 7
6. Question
Find the height, `h cm`, of the trapezium. (`1` decimal place)
- `h=` (3.3)`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, form a triangle using the trapezium.
Identify the parts of the triangle using the given values.Reference angle:Notice that from the given obtuse angle, a right angle was formed as the triangle was drawn.Subtract the right angle from the obtuse angle to find the reference angle of the triangle.`151°7′-90°=61°7’`
Opposite Side:Subtract the two bases of the trapezium to find the opposite side to the reference angle in the triangle.`18 cm-12 cm=6 cm`
Adjacent Side:The side `h` of the trapezium is equal to the adjacent side to the reference angle of the triangle.
Since we now have the opposite and adjacent values, we can use the `tan` ratio to find `h`.$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{6}$$$$\color{#00880a}{\text{adjacent}}=\color{#00880a}{h}$$`tan61°7’` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan61°7’` `=` $$\frac{\color{#004ec4}{6}}{\color{#00880a}{h}}$$ `h` `=` `6/(tan61°7′)` Swap the value on the left side and the denominator from the right side Simplify this further by evaluating `tan61°7’` using the calculator:`1.` Press `tan``2.` Press `61` and DMS or `° ‘ ‘ ‘``3.` Press `7` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `1.812743`Continue solving for `h`.`tan61°7’=1.812743``h` `=` `6/(tan61°7′)` `=` `6/1.812743` `=` `3.3099` `=` `3.3 cm` Rounded off to `1` decimal place 
`3.3 cm` -
Question 7 of 7
7. Question
A wedge-shaped ramp is set up for a car stunt on a movie set. The ramp has an angle of inclination of `19°48’` and a vertical rise of `2.6 m`. Find the length of the ramp (`x`) to the nearest metre.
- `x=` (8)`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 functionNotice that the scenario creates a triangle. Label it in reference to the given angle.
$$\color{#004ec4}{\text{opposite}}=\color{#004ec4}{2.6}$$$$\color{#e85e00}{\text{hypotenuse}}=\color{#e85e00}{x}$$Since we now have the opposite and hypotenuse values, we can use the `sin` ratio to find `x`.`sin19°48’` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin19°48’` `=` $$\frac{\color{#004ec4}{2.6}}{\color{#e85e00}{x}}$$ `x` `=` `2.6/(sin19°48′)` Swap the value on the left side and the denominator from the right side Simplify this further by evaluating `sin19°48’` using the calculator:`1.` Press `sin``2.` Press `19` and DMS or `° ‘ ‘ ‘``3.` Press `48` and DMS or `° ‘ ‘ ‘` again`4.` Press `=`The result will be: `0.338738`Continue solving for `x`.`sin19°48’=0.338738``x` `=` `2.6/(sin19°48′)` `=` `2.6/0.338738` `=` `7.67` `=` `8 m` Rounded off to the nearest metre 
`8 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)