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Trigonometry Mixed Review: Part 2>
Trigonometry Mixed Review: Part 2 (3)Trigonometry Mixed Review: Part 2 (3)
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Question 1 of 7
1. Question
Find the length of `a`
Round your answer to two decimal places- `a=` (12.48)`\text(m)`
Hint
Help VideoCorrect
Well Done!
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` `=` `9.2^2``+``5.4^2``-2``(9.2)``(5.4)``xxcos``115°` Plug in the values `a^2` `=` `84.6+29.16-99.36xxcos115°` Evaluate `a^2` `=` `155.79` `sqrt(a^2)` `=` `sqrt(155.79)` Take the square root of both sides `a` `=` `12.48 m` Rounded to two decimal places `a=12.48 \text(m)` -
Question 2 of 7
2. Question
Solve for angle `C`
Round your answer to the nearest minute- `∠C=` (34)`°` (3)`'`
Hint
Help VideoCorrect
Fantastic!
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` `=` $$\frac{\color{#004ec4}{5^2}+\color{#00880a}{7^2}-\color{#e85e00}{4^2}}{2\color{#004ec4}{(5)}\color{#00880a}{(7)}}$$ Plug in known values `cos``C` `=` `(25+49-16)/(70)` Evaluate `cos``C` `=` `0.8286` Use the inverse function for `cos` on your calculator to get `C` by itself`C` `=` `cos^-1(0.8286)` The inverse of `cos` is `cos^-1` `C` `=` `34.0448084` Use the shift `cos` function on your calculator `C` `=` `34° 2′ 41.31”` Use the degrees button on your calculator `C` `=` `34° 3’` Round up the minutes `C=34° 3’` -
Question 3 of 7
3. Question
Solve for the following values:`(i)` side `a``(ii)` angle `B``(iii)` angle `C`
The given measurements are in unitsRound your answer for the angles to nearest decimal degree-
`a= ` (34)`\text(units)`
`∠B = ` (26)°
`∠C = ` (58)°
Correct
Excellent!
Incorrect
Cosine Rule (finding a length)
`a^2``=``b^2``+``c^2``-2``b``c``xx cos``A`Cosine Rule (finding an angle)
$$cos\color{#00880a}{B}=\frac{\color{#004ec4}{a^2}+\color{#e85e00}{c^2}-\color{#00880a}{b^2}}{2\color{#004ec4}{a}\color{#e85e00}{c}}$$Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
`\text(Solving for) (i) \text(side) a`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` `=` `15^2``+``29^2``-2``(15)``(29)``xxcos``96°` Plug in the values `a^2` `=` `225+841-870xxcos96°` Evaluate `a^2` `=` `1156.939763` `sqrt(a^2)` `=` `sqrt(1156.939763)` Take the square root of both sides `a` `=` `34.0 \text(units)` Rounded to one decimal place `\text(Solving for) (ii) \text(angle) B`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` `=` $$\frac{\color{#004ec4}{29^2}+\color{#e85e00}{34^2}-\color{#00880a}{15^2}}{2\color{#004ec4}{(29)}\color{#e85e00}{(34)}}$$ Plug in known values `cos``B` `=` `(841+1156 –224)/(1972)` Evaluate `cos``B` `=` `0.8990872211` Use the inverse function for `cos` on your calculator to get `B` by itself`B` `=` `cos^-1(0.8990872211)` The inverse of `cos` is `cos^-1` `B` `=` `25.9616553` Use the shift `cos` function on your calculator `B` `=` `26.0°` Rounded to one decimal place `\text(Solving for) (iii) \text(angle) C`We can subtract the total of the known values of the angles to `180°` to find angle `C``C` `=` `180-(``96``+``26``)` Plug in the known values `C` `=` `180-122` Evaluate `C` `=` `58°` `a=34 \text(units)``∠B=26°``∠C=58°` -
`a= ` (34)`\text(units)`
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Question 4 of 7
4. Question
Solve for angle `theta`
Round your answer to the nearest minute- `∠theta=` (112)`°` (59)`'`
Hint
Help VideoCorrect
Well Done!
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 `P``p/sinP` `=` `r/sinR` Sine Rule Formula `210/sinP` `=` `100/(sin26°)` Plug in the values `sin``P`` xx 100` `=` `210 xx sin26°` Cross multiply `sin``P` `=` `(210 xx sin26°)/100` Divide `100` from each side to isolate `sinA` `sin``P` `=` `0.9206` Evaluate Use the inverse function for `sin` on your calculator to get `P` by itself`P` `=` `sin^-1(0.9206)` The inverse of `sin` is `sin^-1` `P` `=` `67.01395604` Use the shift `sin` function on your calculator `P` `=` `67° 0′ 40”` Use the degrees button on your calculator `P` `=` `67°01’` Round up the minutes `theta` should be an obtuse angle, so subtract the value of `P` from `180°`, which is the total interior angle of a triangle`theta` `=` `180-``P` `theta` `=` `180-``67°01’` `theta` `=` `112°59’` `∠theta=112°59’` -
Question 5 of 7
5. Question
Solve for the following values:`(i)` angle `B``(ii)` angle `A``(iii)` side `a`
The given measurements are in unitsRound your answer to one decimal degree-
`∠B = ` (65.9)`˚`
`∠A = ` (29.9)`˚`
`a = ` (14, 14.0)`\text(units)`
Correct
Exceptional!
Incorrect
Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
`\text(Solving for) (i) \text(angle) B`We can use the Sine Rule to find angle `B``b/sinB` `=` `c/sinC` Sine Rule Formula `25.7/sinB` `=` `28/(sin84.2°)` Plug in the values `sin``B`` xx 28` `=` `25.7 xx sin84.2°` Cross multiply `sin``B` `=` `(25.7 xx sin84.2°)/28` Divide `28` from each side to isolate `sinB` `sin``B` `=` `0.913` Evaluate Use the inverse function for `sin` on your calculator to get `B` by itself`B` `=` `sin^-1(0.913)` The inverse of `sin` is `sin^-1` `B` `=` `65.9232` Use the shift `sin` function on your calculator `B` `=` `65.9°` Rounded to one decimal place `\text(Solving for) (ii) \text(angle) A`We can subtract the total of the known values of the angles to `180°` to find angle `A``A` `=` `180-(``84.2``+``65.9``)` Plug in the known values `A` `=` `180-150.1` Evaluate `A` `=` `29.9°` `\text(Solving for) (iii) \text(side) a`Finally, we can use the Sine Rule again to find side `a``a/sinA` `=` `c/sinC` Sine Rule Formula `a/(sin29.9°)` `=` `28/(sin84.2°)` Plug in the values `a``times sin84.2°` `=` `sin29.9° xx 28` Cross multiply `a` `=` `(sin29.9° xx 28)/(sin84.2°)` Divide `sin84.2°` from each side to isolate `a` `a` `=` `14.0 \text(units)` Rounded to one decimal place `∠B=65.9°``∠A=29.9°``a=14 \text(units)` -
`∠B = ` (65.9)`˚`
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Question 6 of 7
6. Question
Solve for angle `B`
Round your answer to the nearest degree- `∠B=` (39)`°`
Correct
Nice Job!
Incorrect
Cosine Rule (finding a length)
`a^2``=``b^2``+``c^2``-2``b``c``xx cos``A`Cosine Rule (finding an angle)
$$cos\color{#00880a}{B}=\frac{\color{#004ec4}{a^2}+\color{#e85e00}{c^2}-\color{#00880a}{b^2}}{2\color{#004ec4}{a}\color{#e85e00}{c}}$$Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
First, we find the length of `a` by using the Cosine Rule (finding a length)`a^2` `=` `b^2``+``c^2``-2``b``c``xxcos``A` Cosine Rule Formula `a^2` `=` `24^2``+``27^2``-2``(24)``(27)``xxcos``96°` Plug in the values `a^2` `=` `576+729-1296xxcos96°` Evaluate `a^2` `=` `1440.468888` `sqrt(a^2)` `=` `sqrt(1440.468888)` Take the square root of both sides `a` `=` `37.95` Rounded to two decimal places Now, 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` `=` $$\frac{\color{#004ec4}{27^2}+\color{#e85e00}{37.95^2}-\color{#00880a}{24^2}}{2\color{#004ec4}{(27)}\color{#e85e00}{(37.95)}}$$ Plug in known values `cos``B` `=` `(729+1440.2025-576)/(2049.3)` Evaluate `cos``B` `=` `0.7774374177` Use the inverse function for `cos` on your calculator to get `B` by itself`B` `=` `cos^-1(0.7774374177)` The inverse of `cos` is `cos^-1` `B` `=` `38.9734571` Use the shift `cos` function on your calculator `B` `=` `39°` Rounded to the nearest whole number `B=39°` -
Question 7 of 7
7. Question
Solve for angle `C`
Round your answer to one decimal degree- `∠C=` (40.8)`°`
Correct
Correct!
Incorrect
Cosine Rule (finding a length)
`b^2``=``a^2``+``c^2``-2``a``c``xx cos``B`Cosine Rule (finding an angle)
$$cos\color{#e85e00}{C}=\frac{\color{#004ec4}{a^2}+\color{#00880a}{b^2}-\color{#e85e00}{c^2}}{2\color{#004ec4}{a}\color{#00880a}{b}}$$Remember
- Uppercase letters represent angles in the triangle
- Lowercase letters represent the side lengths
Labelling the triangle
First, we find the length of `b` by using the Cosine Rule (finding a length)`b^2` `=` `a^2``+``c^2``-2``a``c``xx cos``B` Cosine Rule Formula `b^2` `=` `22.3^2``+``20^2``-2``(22.3)``(20)``xx cos``92.4°` Plug in the values `b^2` `=` `497.29+400-892xxcos92.4°` Evaluate `b^2` `=` `934.6430831` `sqrt(b^2)` `=` `sqrt(934.6430831)` Take the square root of both sides `b` `=` `30.57` Rounded to two decimal places Now, 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` `=` $$\frac{\color{#004ec4}{22.3^2}+\color{#00880a}{30.57^2}-\color{#e85e00}{20^2}}{2\color{#004ec4}{(22.3)}\color{#00880a}{(30.57)}}$$ Plug in known values `cos``C` `=` `(497.29+934.5249 –400)/(1363.422)` Evaluate `cos``C` `=` `0.7567832263` Use the inverse function for `cos` on your calculator to get `C` by itself`C` `=` `cos^-1(0.7567832263)` The inverse of `cos` is `cos^-1` `C` `=` `40.81857096` Use the shift `cos` function on your calculator `C` `=` `40.8°` Rounded to one decimal place `C=40.8°`
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)