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Trigonometry Mixed Review: Part 2>
Trigonometry Mixed Review: Part 2 (1)Trigonometry Mixed Review: Part 2 (1)
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Question 1 of 8
1. Question
Solve for side `a`
Round your answer as a whole number- `a = ` (13) `m`
Hint
Help VideoCorrect
Well Done!
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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/(sin24°)` `=` `23/(sin46°)` Plug in the values `a``times sin46°` `=` `sin24° xx 23` Cross multiply `a` `=` `(sin24° xx 23)/(sin46°)` Divide `sin46°` from each side to isolate `a` `a` `=` `13 m` Rounded to a whole number `a=13 m` -
Question 2 of 8
2. Question
Solve for angle `Z`
Round your answer to the nearest degree- `∠Z=` (36)`°`
Hint
Help VideoCorrect
Keep Going!
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 `Z``y/sinY` `=` `z/sinZ` Sine Rule Formula `39.7/(sin122°)` `=` `27.5/sinZ` Plug in the values `sin``Z`` xx 39.7` `=` `27.5 xx sin122°` Cross multiply `sin``Z` `=` `(27.5 xx sin122°)/39.7` Divide `39.7` from each side to isolate `sinA` `sin``Z` `=` `0.5874` Evaluate Use the inverse function for `sin` on your calculator to get `Z` by itself`Z` `=` `sin^-1(0.5874)` The inverse of `sin` is `sin^-1` `Z` `=` `35.9727` Use the shift `sin` function on your calculator `Z` `=` `36°` Rounded to the nearest degree `∠Z=36°` -
Question 3 of 8
3. Question
Find the length of `a`
Round your answer as a whole number- `a=` (41)`\text(m)`
Hint
Help VideoCorrect
Keep Going!
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` `=` `26^2``+``21^2``-2``(26)``(21)``xxcos``121°` Plug in the values $$ a^2$$ `=` `441+676-1092xxcos121°` Evaluate `a^2` `=` `1679.421578` `sqrt(a^2)` `=` `sqrt(1679.421578)` Take the square root of both sides `a` `=` `41` Rounded to a whole number `a=41 \text(m)` -
Question 4 of 8
4. Question
Solve for angle `B`
Round your answer to the nearest minute- `∠B=` (87)`°` (16)`'`
Hint
Help VideoCorrect
Well Done!
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` `=` $$\frac{\color{#004ec4}{7^2}+\color{#e85e00}{6^2}-\color{#00880a}{9^2}}{2\color{#004ec4}{(7)}\color{#e85e00}{(6)}}$$ Plug in known values `cos``B` `=` `(49+36-81)/(84)` Evaluate `cos``B` `=` `0.0476` Use the inverse function for `cos` on your calculator to get `B` by itself`B` `=` `cos^-1(0.0476)` The inverse of `cos` is `cos^-1` `B` `=` `87.27` Use the shift `cos` function on your calculator `B` `=` `87° 16′ 12”` Use the degrees button on your calculator `B` `=` `87° 16’` Round up the minutes `B=87° 16’` -
Question 5 of 8
5. Question
Solve for side `a`
Round your answer to two decimal places- `a = ` (28.73) `cm`
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 `a``a/sinA` `=` `c/sinC` Sine Rule Formula `a/(sin67°)` `=` `17/(sin33°)` Plug in the values `a``times sin33°` `=` `sin67° xx 17` Cross multiply `a` `=` `(sin67° xx 17)/(sin33°)` Divide `sin33°` from each side to isolate `a` `a` `=` `28.73 cm` Rounded to two decimal places `a=28.73 cm` -
Question 6 of 8
6. Question
Find the length of `c`
Round your answer as a whole number- `c=` (39)`\text(cm)`
Correct
Correct!
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 a length) to find the length of `c``c^2` `=` `a^2``+``b^2``-2``a``b``xx cos``C` Cosine Rule Formula `c^2` `=` `18^2``+``28^2``-2``(18)``(28)``xx cos``144°` Plug in the values `c^2` `=` `324+784-1008xxcos144°` Evaluate `c^2` `=` `1517.990536` `sqrt(c^2)` `=` `sqrt(1517.990536)` Take the square root of both sides `c` `=` `39 cm` Rounded to a whole number `c=39 \text(cm)` -
Question 7 of 8
7. Question
Solve for side `c`
Round your answer to two decimal places- `c = ` (7.35) `km`
Hint
Help VideoCorrect
Fantastic!
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 `c``b/sinB` `=` `c/sinC` Sine Rule Formula `5.8/(sin47°)` `=` `c/(sin68°)` Plug in the values `c``times sin47°` `=` `sin68° xx 5.8` Cross multiply `c` `=` `(sin68° xx 5.8)/(sin47°)` Divide `sin47°` from each side to isolate `c` `c` `=` `7.35 km` Rounded to two decimal places `c=7.35 km` -
Question 8 of 8
8. Question
Solve for angle `B`
Round your answer to the nearest decimal degree- `∠B=` (38)`°`
Correct
Great Work!
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 `11/sinB` `=` `17/(sin108°)` Plug in the values `sin``B`` xx 17` `=` `11 xx sin108°` Cross multiply `sin``B` `=` `(11 xx sin108°)/17` Divide `17` from each side to isolate `sinB` `sin``B` `=` `0.615` Evaluate Use the inverse function for `sin` on your calculator to get `B` by itself`B` `=` `sin^-1(0.615)` The inverse of `sin` is `sin^-1` `B` `=` `37.951` Use the shift `sin` function on your calculator `B` `=` `38°` Rounded to a whole number `∠B=38°`
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)