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Trigonometry Mixed Review: Part 1>
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Question 1 of 8
1. Question
Solve for `theta`
Round your answer to the nearest minute- `theta=` (35)`°` (55)`'`
Hint
Help VideoCorrect
Great Work!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(29)` is `\text(adjacent)` to `theta` and the other length `(21)` is `\text(opposite)` to `theta`
Hence, we can use the `tan \text(ratio)` to solve for `theta``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan theta` `=` $$\frac{\color{#004ec4}{21}}{\color{#00880a}{29}}$$ Plug in the values `tan theta` `=` `0.724` Use the inverse function for `tan` on your calculator to get `theta` by itself`theta` `=` `tan^(-1) (0.724)` The inverse of `tan` is `tan^(-1)` `theta` `=` `35.9097` Use the `\text(shift) tan` function on your calculator `theta` `=` `35°54’35”` Use the `\text(degrees)` function on your calculator `theta` `=` `35°55’` Rounded to the nearest minute `theta=35°55’` -
Question 2 of 8
2. Question
Solve for `x`
Round your answer to one decimal place- `x =` (25.3)
Correct
Excellent!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known angles `(56°)` has `21` as an `\text(opposite)` side and `x` is the `\text(hypotenuse)`
Hence, we can use the `sin \text(ratio)` to solve for `x``sin theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `sin \text(ratio)` `sin (56°)` `=` $$\frac{\color{#004ec4}{21}}{\color{#e85e00}{x}}$$ Plug in the values Get `x` by itself to find its value`sin (56°)` `=` `21/x` `x xx sin (56°)` `=` `21` Multiply both sides by `x` `x` `=` `21/sin (56°)` Divide both sides by `sin(56°)` `x` `=` `21/0.8290375726` Evaluate `sin(56°)` on the calculator `x` `=` `25.3` Round to one decimal place `x=25.3` -
Question 3 of 8
3. Question
Solve for `theta`
Round your answer to the nearest degree- `theta=` (73)`°`
Correct
Keep Going!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(8)` is `\text(adjacent)` to `theta` and the other length `(28)` is the `\text(hypotenuse)`
Hence, we can use the `cos \text(ratio)` to solve for `theta``cos theta` `=` $$\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$ `cos \text(ratio)` `cos theta` `=` $$\frac{\color{#00880a}{8}}{\color{#e85e00}{28}}$$ Plug in the values `cos theta` `=` `0.286` Use the inverse function for `cos` on your calculator to get `theta` by itself`theta` `=` `cos^(-1) (0.286)` The inverse of `cos` is `cos^(-1)` `theta` `=` `73.381°` Use the `\text(shift) cos` function on your calculator `theta` `=` `73°` Rounded to the nearest degree `theta=73°` -
Question 4 of 8
4. Question
Find the length of `d`
The given measurements are in metresRound your answer to the nearest whole number- `d=` (139) m
Hint
Help VideoCorrect
Fantastic!
Incorrect
The Angles of Elevation and Depression are the angles created by the upward or downward slope of the hypotenuse.The lines on top and bottom of the building are parallel, and the hypotenuse that cuts through it creates an angle of depression measured `47°10’`
Since the angle of elevation (`theta`) is opposite of the angle of depression
(`47°10’`), `theta` is also equal to `47°10’`Next, we need to identify which trig ratio to use.Angle `theta` has `150 m` as an `\text(opposite)` side and `d` as an `\text(adjacent)` side.
Hence, we can use the `tan \text(ratio)` to solve for `d``tan``theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan``47˚10’` `=` $$\frac{\color{#004ec4}{150}}{\color{#00880a}{d}}$$ Plug in the values `d xx 1.0786` `=` `150` Cross multiply `d` `=` `150/1.0786` Divide `1.0786` from both sides to isolate `d` `d` `=` `139 m` `d=139 m` -
Question 5 of 8
5. Question
Find the area of the Triangle
The given measurements are in unitsRound your answer to one decimal place- `\text(Area )=` (32.6)`units^2`
Correct
Nice Job!
Incorrect
Area of a Triangle Formula
`\text(Area )=1/2 xx``b``times``c``times sin``A`
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
Solve for the area using the Area of a Triangle formula`A` `=` `1/2 xx``b``times``c``times sin``A` Area of a Triangle formula `=` `1/2 xx``11.5``times``7``times sin``126°` Plug in the known lengths `=` `32.6 units^2` Rounded to one decimal place The given measurements are in units, so the area is measured as square units`\text(Area)=32.6 units^2` -
Question 6 of 8
6. Question
Solve for `theta`
Round your answer to the nearest minuteHint
Help VideoCorrect
Exceptional!
Incorrect
Sin Ratio
$$sin=\frac{\color{#004ec4}{\text{opposite}}}{\color{#e85e00}{\text{hypotenuse}}}$$Cos Ratio
$$cos=\frac{\color{#00880a}{\text{adjacent}}}{\color{#e85e00}{\text{hypotenuse}}}$$Tan Ratio
$$tan=\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$First we need to identify which trig ratio to use.One of the known lengths `(4.9)` is `\text(opposite)` to `theta`, and the other length `(10.6)` is `\text(adjacent)` to `theta`, but we only need half of that length to form a right triangle.
`\text(adjacent)` `=` `10.6divide2` `\text(adjacent)` `=` `5.3` Hence, we can use the `tan \text(ratio)` to solve for `theta``tan theta` `=` $$\frac{\color{#004ec4}{\text{opposite}}}{\color{#00880a}{\text{adjacent}}}$$ `tan \text(ratio)` `tan theta` `=` $$\frac{\color{#004ec4}{4.9}}{\color{#00880a}{5.3}}$$ Plug in the values `tan theta` `=` `0.9243` Use the inverse function for `tan` on your calculator to get `theta` by itself`theta` `=` `tan^(-1) (0.9243)` The inverse of `tan` is `tan^(-1)` `theta` `=` `42.7543` Use the `\text(shift) tan` function on your calculator `theta` `=` `42°45’15”` Use the `\text(degrees)` function on your calculator `theta` `=` `42°45’` Rounded to the nearest minute `theta=42°45’` -
Question 7 of 8
7. Question
Find the area of the Triangle
The given measurements are in unitsRound your answer to the nearest whole number- `\text(Area )=` (47)`units^2`
Correct
Correct!
Incorrect
Area of a Triangle Formula
`\text(Area )=1/2 xx``a``times``c``times sin``B`Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
First, we need to find an angle between two sides with known values.We can use the Sine Rule to find angle `C``a/sinA` `=` `c/sinC` Sine Rule Formula `14/(sin77°)` `=` `7/sinC` Plug in the values `sin``C`` xx 14` `=` `7 xx sin77°` Cross multiply `sin``C` `=` `(7 xx sin77°)/14` Divide `14` from each side to isolate `sinC` `sin``C` `=` `6.821/14` Simplify `sin``C` `=` `0.487` Use the inverse function for `sin` on your calculator to get `C` by itself`C` `=` `sin^-1(0.487)` The inverse of `sin` is `sin^-1` `C` `=` `29.155` Use the shift `sin` function on your calculator `C` `=` `29.2°` Rounded to one decimal place Now that we have the value of `C`, we can get the value of `B` by subtracting the total value of `A` and `C` to `180°`, the total interior angle of a triangle`B` `=` `180°-(``A``+``C``)` `B` `=` `180°-(``77``+``29.2``)` Plug in the known values `B` `=` `73.8°` Finally, solve for the area using the Area of a Triangle formula`\text(Area)` `=` `1/2 xx``a``times``c``times sin``B` Area of a Triangle formula `=` `1/2 xx``14``times``7``times sin``73.8°` Plug in the known lengths `=` `47.0 units^2` Rounded to one decimal place The given measurements are in units, so the area is measured as square units`\text(Area)=47 units^2` -
Question 8 of 8
8. Question
Find the area of the Triangle
The given measurements are in unitsRound your answer to the nearest whole number- `\text(Area )=` (92)`units^2`
Correct
Great Work!
Incorrect
Area of a Triangle Formula
`\text(Area )=1/2 xx``b``times``c``times sin``A`Cosine Rule (finding an angle)
$$cos\color{#004ec4}{A}=\frac{\color{#00880a}{b^2}+\color{#e85e00}{c^2}-\color{#004ec4}{a^2}}{2\color{#00880a}{b}\color{#e85e00}{c}}$$Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
First, we need to find an angle to use for the Area of a Triangle formulaWe can use the Cosine Rule (finding an angle) to solve for `A``cos``A` `=` $$\frac{\color{#00880a}{b^2}+\color{#e85e00}{c^2}-\color{#004ec4}{a^2}}{2\color{#00880a}{b}\color{#e85e00}{c}}$$ Cosine Rule Formula `cos``A` `=` $$\frac{\color{#00880a}{13.9^2}+\color{#e85e00}{14^2}-\color{#004ec4}{16^2}}{2\color{#00880a}{(13.9)}\color{#e85e00}{(14)}}$$ Plug in known values `cos``A` `=` `(193.21+196-256)/(389.2)` Evaluate `cos``A` `=` `0.342` Use the inverse function for `cos` on your calculator to get `A` by itself`A` `=` `cos^-1(0.342)` The inverse of `cos` is `cos^-1` `A` `=` `71.094` Use the shift `cos` function on your calculator `A` `=` `71.1°` Rounded to one decimal place Finally, solve for the area using the Area of a Triangle formula`A` `=` `1/2 xx``b``times``c``times sin``A` Area of a Triangle formula `=` `1/2 xx``13.9``times``14``times sin``71.1°` Plug in the known lengths `=` `92 units^2` Rounded to one decimal place The given measurements are in units, so the area is measured as square units`\text(Area)=92 units^2`
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)