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Trigonometry Mixed Review: Part 2>
Trigonometry Mixed Review: Part 2 (2)Trigonometry Mixed Review: Part 2 (2)
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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
- Law of Sines: Solving for a Side
- Law of Sines: Solving for an Angle
- Law of Cosines: Solving for a Side
- Law of Cosines: 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)