Years
>
Year 11>
Trigonometry>
Trigonometry Mixed Review: Part 2>
Trigonometry Mixed Review: Part 2 (2)Trigonometry Mixed Review: Part 2 (2)
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 7 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
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
- 6
- 7
- Answered
- Review
-
Question 1 of 7
1. Question
Solve for angle `B`
Round your answer to one decimal degree- `∠B=` (25.9)`°`
Correct
Nice Job!
Incorrect
Cosine Rule (finding a length)
`b^2``=``a^2``+``c^2``-2``a``c``xx cos``B`Cosine Rule (finding an angle)
$$cos\color{#00880a}{B}=\frac{\color{#004ec4}{a^2}+\color{#e85e00}{c^2}-\color{#00880a}{b^2}}{2\color{#004ec4}{a}\color{#e85e00}{c}}$$
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Cosine Rule (finding an angle) to solve for `B``cos``B` `=` $$\frac{\color{#004ec4}{a^2}+\color{#e85e00}{c^2}-\color{#00880a}{b^2}}{2\color{#004ec4}{a}\color{#e85e00}{c}}$$ Cosine Rule Formula `cos``B` `=` $$\frac{\color{#004ec4}{25.4^2}+\color{#e85e00}{17.3^2}-\color{#00880a}{12.4^2}}{2\color{#004ec4}{(25.4)}\color{#e85e00}{(12.4)}}$$ Plug in known values `cos``B` `=` `(645.16+299.29-153.76)/(878.84)` Evaluate `cos``B` `=` `0.8996973283` Use the inverse function for `cos` on your calculator to get `B` by itself`B` `=` `cos^-1(0.8996973283)` The inverse of `cos` is `cos^-1` `B` `=` `25.88168913` Use the shift `cos` function on your calculator `B` `=` `25.9°` Rounded to one decimal place `B=25.9°` -
Question 2 of 7
2. Question
Solve for angle `B`
Round your answer to one decimal degree- `∠B=` (58.1)`°`
Correct
Correct!
Incorrect
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Sine Rule to find angle `B``b/sinB` `=` `c/sinC` Sine Rule Formula `28/sinB` `=` `31/(sin70°)` Plug in the values `sin``B`` xx 31` `=` `28 xx sin70°` Cross multiply `sin``B` `=` `(28 xx sin70°)/31` Divide `31` from each side to isolate `sinB` `sin``B` `=` `0.849` Evaluate Use the inverse function for `sin` on your calculator to get `B` by itself`B` `=` `sin^-1(0.849)` The inverse of `sin` is `sin^-1` `B` `=` `58.1030` Use the shift `sin` function on your calculator `B` `=` `58.1°` Rounded to one decimal place `∠B=58.1°` -
Question 3 of 7
3. Question
Solve for angle `A`
Round your answer to the nearest minute- `∠A=` (61)`°` (45)`'`
Hint
Help VideoCorrect
Excellent!
Incorrect
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Sine Rule to find angle `A``a/sinA` `=` `c/sinC` Sine Rule Formula `12.5/sinA` `=` `8.4/(sin36°18′)` Plug in the values `sin``A`` xx 8.4` `=` `12.5 xx sin36°18’` Cross multiply `sin``A` `=` `(12.5 xx sin36°18′)/8.4` Divide `8.4` from each side to isolate `sinA` `sin``A` `=` `0.88097` Evaluate Use the inverse function for `sin` on your calculator to get `A` by itself`A` `=` `sin^-1(0.88097)` The inverse of `sin` is `sin^-1` `A` `=` `61.75959621` Use the shift `sin` function on your calculator `A` `=` `61° 45′ 34.55”` Use the degrees button on your calculator `A` `=` `61°45’` Round up the minutes `∠A=61°45’` -
Question 4 of 7
4. Question
Solve for side `a`
Round your answer as a whole number- `a = ` (34) `km`
Correct
Nice Job!
Incorrect
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Sine Rule to find side `a``a/sinA` `=` `c/sinC` Sine Rule Formula `a/(sin96°)` `=` `15/(sin26°)` Plug in the values `a``times sin26°` `=` `sin96° xx 15` Cross multiply `a` `=` `(sin96° xx 15)/(sin26°)` Divide `sin26°` from each side to isolate `a` `a` `=` `34 km` Rounded to a whole number `a=34 km` -
Question 5 of 7
5. Question
Solve for angle `C`
Round your answer to one decimal degree- `∠C=` (101.2)`°`
Correct
Excellent!
Incorrect
Cosine Rule (finding a length)
`c^2``=``a^2``+``b^2``-2``a``b``xx cos``C`Cosine Rule (finding an angle)
$$cos\color{#e85e00}{C}=\frac{\color{#004ec4}{a^2}+\color{#00880a}{b^2}-\color{#e85e00}{c^2}}{2\color{#004ec4}{a}\color{#00880a}{b}}$$Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Cosine Rule (finding an angle) to solve for `C``cos``C` `=` $$\frac{\color{#004ec4}{a^2}+\color{#00880a}{b^2}-\color{#e85e00}{c^2}}{2\color{#004ec4}{a}\color{#00880a}{b}}$$ Cosine Rule Formula `cos``C` `=` $$\frac{\color{#004ec4}{8^2}+\color{#00880a}{19^2}-\color{#e85e00}{22^2}}{2\color{#004ec4}{(8)}\color{#00880a}{(19)}}$$ Plug in known values `cos``C` `=` `(64+361-484)/(304)` Evaluate `cos``C` `=` `-0.19407` Use the inverse function for `cos` on your calculator to get `C` by itself`C` `=` `cos^-1(-0.19407)` The inverse of `cos` is `cos^-1` `C` `=` `101.190923` Use the shift `cos` function on your calculator `C` `=` `101.2°` Rounded to one decimal place `C=101.2°` -
Question 6 of 7
6. Question
Find the length of `a`
Round your answer to one decimal place- `a=` (15.3)`\text(cm)`
Hint
Help VideoCorrect
Great Work!
Incorrect
Cosine Rule (finding a length)
`a^2``=``b^2``+``c^2``-2``b``c``xx cos``A`Cosine Rule (finding an angle)
$$cos\color{#004ec4}{A}=\frac{\color{#004ec4}{a^2}+\color{#00880a}{b^2}-\color{#e85e00}{c^2}}{2\color{#004ec4}{a}\color{#00880a}{b}}$$Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Cosine Rule (finding a length) to find the length of `a``a^2` `=` `b^2``+``c^2``-2``b``c``xxcos``A` Cosine Rule Formula `a^2` `=` `17^2``+``20^2``-2``(17)``(20)``xxcos``48°` Plug in the values `a^2` `=` `289+400-680xxcos48°` Evaluate `a^2` `=` `234` `sqrt(a^2)` `=` `sqrt(234)` Take the square root of both sides `a` `=` `15.3 cm` Rounded to a whole number `a=15.3 \text(cm)` -
Question 7 of 7
7. Question
Solve for side `x`
Round off answer to `1` decimal place- `x = ` (13.3) `m`
Correct
Excellent!
Incorrect
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
We can use the Sine Rule to find side `x``x/sinX` `=` `z/sinZ` Sine Rule Formula `x/(sin42°)` `=` `18/(sin65°)` Plug in the values `x``times sin65°` `=` `sin42° xx 18` Cross multiply `x` `=` `(sin42° xx 18)/(sin65°)` Divide `sin46°` from each side to isolate `x` `x` `=` `13.3 m` Rounded to `1` decimal place `x=13.3 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)