Trigonometry Mixed Review: Part 2 (1)

Question 1 of 8

Solve for side

a

$a$

Round your answer as a whole number

$a =$ $a =$ (13) $m$ $m$

Question 2 of 8

Solve for angle

Z

$Z$

Round your answer to the nearest degree

$∠ Z =$ $∠Z=$ (36) $°$ $°$

Question 3 of 8

Find the length of

a

$a$

Round your answer as a whole number

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

Incorrect

Cosine Rule (finding a length)

$a^{2}$ $a^2$

=

$=$ $b^{2}$ $b^2$

+

$+$ $c^{2}$ $c^2$

- 2

$-2$ $b$ $b$ $c$ $c$

\times cos

$xx cos$ $A$ $A$

Cosine Rule (finding an angle)

c o s A = \frac{a^{2} + b^{2} - c^{2}}{2 a b}

$cos\color{#004ec4}{A}=\frac{\color{#004ec4}{a^2}+\color{#00880a}{b^2}-\color{#e85e00}{c^2}}{2\color{#004ec4}{a}\color{#00880a}{b}}$

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 $a$ $a$

$a^{2}$ $a^2$	$=$ $=$	$b^{2}$ $b^2$ $+$ $+$ $c^{2}$ $c^2$ $- 2$ $-2$ $b$ $b$ $c$ $c$ $\times cos$ $xxcos$ $A$ $A$	Cosine Rule Formula
$a^{2}$ $a^2$	$=$ $=$	$26^{2}$ $26^2$ $+$ $+$ $21^{2}$ $21^2$ $- 2$ $-2$ $(26)$ $(26)$ $(21)$ $(21)$ $\times cos$ $xxcos$ $121 °$ $121°$	Plug in the values
$a^2$	$=$ $=$	$441 + 676 - 1092 \times cos 121 °$ $441+676-1092xxcos121°$	Evaluate
$a^{2}$ $a^2$	$=$ $=$	$1679.421578$ $1679.421578$
$\sqrt{a^{2}}$ $sqrt(a^2)$	$=$ $=$	$\sqrt{1679.421578}$ $sqrt(1679.421578)$	Take the square root of both sides
$a$ $a$	$=$ $=$	$41$ $41$	Rounded to a whole number

a = 41 m

$a=41 \text(m)$

Question 4 of 8

Solve for angle

B

$B$

Round your answer to the nearest minute

$∠ B =$ $∠B=$ (87) $°$ $°$ (16) $'$ $'$

Incorrect

Cosine Rule (finding a length)

$b^{2}$ $b^2$

=

$=$ $a^{2}$ $a^2$

+

$+$ $c^{2}$ $c^2$

- 2

$-2$ $a$ $a$ $c$ $c$

\times cos

$xx cos$ $B$ $B$

Cosine Rule (finding an angle)

c o s B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}

$cos\color{#00880a}{B}=\frac{\color{#004ec4}{a^2}+\color{#e85e00}{c^2}-\color{#00880a}{b^2}}{2\color{#004ec4}{a}\color{#e85e00}{c}}$

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 $B$ $B$

$cos$ $cos$ $B$ $B$	$=$ $=$	$\frac{\color{#004ec4}{a^2}+\color{#e85e00}{c^2}-\color{#00880a}{b^2}}{2\color{#004ec4}{a}\color{#e85e00}{c}}$	Cosine Rule Formula

$cos$ $cos$ $B$ $B$	$=$ $=$	$\frac{\color{#004ec4}{7^2}+\color{#e85e00}{6^2}-\color{#00880a}{9^2}}{2\color{#004ec4}{(7)}\color{#e85e00}{(6)}}$	Plug in known values

$cos$ $cos$ $B$ $B$	$=$ $=$	$\frac{49 + 36 - 81}{84}$ $(49+36-81)/(84)$	Evaluate

$cos$ $cos$ $B$ $B$	$=$ $=$	$0.0476$ $0.0476$

Use the inverse function for

cos

$cos$ on your calculator to get $B$ $B$ by itself

$B$ $B$	$=$ $=$	${cos}^{- 1} (0.0476)$ $cos^-1(0.0476)$	The inverse of $cos$ $cos$ is ${cos}^{- 1}$ $cos^-1$
$B$ $B$	$=$ $=$	$87.27$ $87.27$	Use the shift $cos$ $cos$ function on your calculator
$B$ $B$	$=$ $=$	$87 ° 16' 12 ”$ $87° 16′ 12”$	Use the degrees button on your calculator
$B$ $B$	$=$ $=$	$87 ° 16 ’$ $87° 16’$	Round up the minutes

B = 87 ° 16 ’

$B=87° 16’$

Question 5 of 8

Solve for side

a

$a$

Round your answer to two decimal places

$a =$ $a =$ (28.73) $c m$ $cm$

Question 6 of 8

Find the length of

c

$c$

Round your answer as a whole number

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

Incorrect

Cosine Rule (finding a length)

$c^{2}$ $c^2$

=

$=$ $a^{2}$ $a^2$

+

$+$ $b^{2}$ $b^2$

- 2

$-2$ $a$ $a$ $b$ $b$

\times cos

$xx cos$ $C$ $C$

Cosine Rule (finding an angle)

c o s C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}

$cos\color{#e85e00}{C}=\frac{\color{#004ec4}{a^2}+\color{#00880a}{b^2}-\color{#e85e00}{c^2}}{2\color{#004ec4}{a}\color{#00880a}{b}}$

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 $c$ $c$

$c^{2}$ $c^2$	$=$ $=$	$a^{2}$ $a^2$ $+$ $+$ $b^{2}$ $b^2$ $- 2$ $-2$ $a$ $a$ $b$ $b$ $\times cos$ $xx cos$ $C$ $C$	Cosine Rule Formula
$c^{2}$ $c^2$	$=$ $=$	$18^{2}$ $18^2$ $+$ $+$ $28^{2}$ $28^2$ $- 2$ $-2$ $(18)$ $(18)$ $(28)$ $(28)$ $\times cos$ $xx cos$ $144 °$ $144°$	Plug in the values
$c^{2}$ $c^2$	$=$ $=$	$324 + 784 - 1008 \times cos 144 °$ $324+784-1008xxcos144°$	Evaluate
$c^{2}$ $c^2$	$=$ $=$	$1517.990536$ $1517.990536$
$\sqrt{c^{2}}$ $sqrt(c^2)$	$=$ $=$	$\sqrt{1517.990536}$ $sqrt(1517.990536)$	Take the square root of both sides
$c$ $c$	$=$ $=$	$39 c m$ $39 cm$	Rounded to a whole number

c = 39 cm

$c=39 \text(cm)$

Question 7 of 8

Solve for side

c

$c$

Round your answer to two decimal places

$c =$ $c =$ (7.35) $k m$ $km$

Question 8 of 8

Solve for angle

B

$B$

Round your answer to the nearest decimal degree

$∠ B =$ $∠B=$ (38) $°$ $°$

$\frac{a}{sin A}$ $a/sinA$	$=$ $=$	$\frac{c}{sin C}$ $c/sinC$	Sine Rule Formula

$\frac{a}{sin 24 °}$ $a/(sin24°)$	$=$ $=$	$\frac{23}{sin 46 °}$ $23/(sin46°)$	Plug in the values

$a$ $a$ $\times sin 46 °$ $times sin46°$	$=$ $=$	$sin 24 ° \times 23$ $sin24° xx 23$	Cross multiply
$a$ $a$	$=$ $=$	$\frac{sin 24 ° \times 23}{sin 46 °}$ $(sin24° xx 23)/(sin46°)$	Divide $sin 46 °$ $sin46°$ from each side to isolate $a$ $a$

$a$ $a$	$=$ $=$	$13 m$ $13 m$	Rounded to a whole number

$\frac{y}{sin Y}$ $y/sinY$	$=$ $=$	$\frac{z}{sin Z}$ $z/sinZ$	Sine Rule Formula

$\frac{39.7}{sin 122 °}$ $39.7/(sin122°)$	$=$ $=$	$\frac{27.5}{sin Z}$ $27.5/sinZ$	Plug in the values

$sin$ $sin$ $Z$ $Z$ $\times 39.7$ $xx 39.7$	$=$ $=$	$27.5 \times sin 122 °$ $27.5 xx sin122°$	Cross multiply

$sin$ $sin$ $Z$ $Z$	$=$ $=$	$\frac{27.5 \times sin 122 °}{39.7}$ $(27.5 xx sin122°)/39.7$	Divide $39.7$ $39.7$ from each side to isolate $sin A$ $sinA$

$sin$ $sin$ $Z$ $Z$	$=$ $=$	$0.5874$ $0.5874$	Evaluate

$\frac{a}{sin A}$ $a/sinA$	$=$ $=$	$\frac{c}{sin C}$ $c/sinC$	Sine Rule Formula

$\frac{a}{sin 67 °}$ $a/(sin67°)$	$=$ $=$	$\frac{17}{sin 33 °}$ $17/(sin33°)$	Plug in the values

$a$ $a$ $\times sin 33 °$ $times sin33°$	$=$ $=$	$sin 67 ° \times 17$ $sin67° xx 17$	Cross multiply
$a$ $a$	$=$ $=$	$\frac{sin 67 ° \times 17}{sin 33 °}$ $(sin67° xx 17)/(sin33°)$	Divide $sin 33 °$ $sin33°$ from each side to isolate $a$ $a$

$a$ $a$	$=$ $=$	$28.73 c m$ $28.73 cm$	Rounded to two decimal places

$\frac{b}{sin B}$ $b/sinB$	$=$ $=$	$\frac{c}{sin C}$ $c/sinC$	Sine Rule Formula

$\frac{5.8}{sin 47 °}$ $5.8/(sin47°)$	$=$ $=$	$\frac{c}{sin 68 °}$ $c/(sin68°)$	Plug in the values

$c$ $c$ $\times sin 47 °$ $times sin47°$	$=$ $=$	$sin 68 ° \times 5.8$ $sin68° xx 5.8$	Cross multiply
$c$ $c$	$=$ $=$	$\frac{sin 68 ° \times 5.8}{sin 47 °}$ $(sin68° xx 5.8)/(sin47°)$	Divide $sin 47 °$ $sin47°$ from each side to isolate $c$ $c$

$c$ $c$	$=$ $=$	$7.35 k m$ $7.35 km$	Rounded to two decimal places

$\frac{b}{sin B}$ $b/sinB$	$=$ $=$	$\frac{c}{sin C}$ $c/sinC$	Sine Rule Formula

$\frac{11}{sin B}$ $11/sinB$	$=$ $=$	$\frac{17}{sin 108 °}$ $17/(sin108°)$	Plug in the values

$sin$ $sin$ $B$ $B$ $\times 17$ $xx 17$	$=$ $=$	$11 \times sin 108 °$ $11 xx sin108°$	Cross multiply

$sin$ $sin$ $B$ $B$	$=$ $=$	$\frac{11 \times sin 108 °}{17}$ $(11 xx sin108°)/17$	Divide $17$ $17$ from each side to isolate $sin B$ $sinB$

$sin$ $sin$ $B$ $B$	$=$ $=$	$0.615$ $0.615$	Evaluate

$Z$ $Z$	$=$ $=$	${sin}^{- 1} (0.5874)$ $sin^-1(0.5874)$	The inverse of $sin$ $sin$ is ${sin}^{- 1}$ $sin^-1$
$Z$ $Z$	$=$ $=$	$35.9727$ $35.9727$	Use the shift $sin$ $sin$ function on your calculator
$Z$ $Z$	$=$ $=$	$36 °$ $36°$	Rounded to the nearest degree

$B$ $B$	$=$ $=$	${sin}^{- 1} (0.615)$ $sin^-1(0.615)$	The inverse of $sin$ $sin$ is ${sin}^{- 1}$ $sin^-1$
$B$ $B$	$=$ $=$	$37.951$ $37.951$	Use the shift $sin$ $sin$ function on your calculator
$B$ $B$	$=$ $=$	$38 °$ $38°$	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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