Trigonometry Mixed Review: Part 2 (1)

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Question 1 of 8

Solve for side

$a$

Round your answer as a whole number

$a =$ (13) $m$

Question 2 of 8

Solve for angle

$Z$

Round your answer to the nearest degree

$∠Z=$ (36) $°$

Question 3 of 8

Find the length of

$a$

Round your answer as a whole number

$a=$ (41) $\text(m)$

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

Solve for angle

$B$

Round your answer to the nearest minute

$∠B=$ (87) $°$ (16) $'$

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

Solve for side

$a$

Round your answer to two decimal places

$a =$ (28.73) $cm$

Question 6 of 8

Find the length of

$c$

Round your answer as a whole number

$c=$ (39) $\text(cm)$

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

Solve for side

$c$

Round your answer to two decimal places

$c =$ (7.35) $km$

Question 8 of 8

Solve for angle

$B$

Round your answer to the nearest decimal degree

$∠B=$ (38) $°$

$a/sinA$	$=$	$c/sinC$	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

$y/sinY$	$=$	$z/sinZ$	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

$a/sinA$	$=$	$c/sinC$	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

$b/sinB$	$=$	$c/sinC$	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

$b/sinB$	$=$	$c/sinC$	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

$Z$	$=$	$sin^-1(0.5874)$	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

$B$	$=$	$sin^-1(0.615)$	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

Trigonometry Mixed Review: Part 2 (1)

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Quiz summary

Information

1. Question

Hint

Well Done!

Remember

Labelling the triangle

2. Question

Hint

Keep Going!

Remember

Labelling the triangle

3. Question

Hint

Keep Going!

Cosine Rule (finding a length)

Cosine Rule (finding an angle)

Remember

Labelling the triangle

4. Question

Hint

Well Done!

Cosine Rule (finding a length)

Cosine Rule (finding an angle)

Remember

Labelling the triangle

5. Question

Excellent!

Remember

Labelling the triangle

6. Question

Correct!

Cosine Rule (finding a length)

Cosine Rule (finding an angle)

Remember

Labelling the triangle

7. Question

Hint

Fantastic!

Remember

Labelling the triangle

8. Question

Great Work!

Remember

Labelling the triangle

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