Trigonometry Mixed Review: Part 2 (2)

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Question 1 of 7

Solve for angle

$B$

Round your answer to one decimal degree

$∠B=$ (25.9) $°$

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

Solve for angle

$B$

Round your answer to one decimal degree

$∠B=$ (58.1) $°$

Question 3 of 7

Solve for angle

$A$

Round your answer to the nearest minute

$∠A=$ (61) $°$ (45) $'$

Question 4 of 7

Solve for side

$a$

Round your answer as a whole number

$a =$ (34) $km$

Question 5 of 7

Solve for angle

$C$

Round your answer to one decimal degree

$∠C=$ (101.2) $°$

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

Find the length of

$a$

Round your answer to one decimal place

$a=$ (15.3) $\text(cm)$

Incorrect

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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

Solve for side

$x$

Round off answer to

$1$ decimal place

$x =$ (13.3) $m$

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

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

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

$x/sinX$	$=$	$z/sinZ$	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

$B$	$=$	$sin^-1(0.849)$	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

$A$	$=$	$sin^-1(0.88097)$	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

Trigonometry Mixed Review: Part 2 (2)

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Quiz summary

Information

1. Question

Nice Job!

Cosine Rule (finding a length)

Cosine Rule (finding an angle)

Remember

Labelling the triangle

2. Question

Correct!

Remember

Labelling the triangle

3. Question

Hint

Excellent!

Remember

Labelling the triangle

4. Question

Nice Job!

Remember

Labelling the triangle

5. Question

Excellent!

Cosine Rule (finding a length)

Cosine Rule (finding an angle)

Remember

Labelling the triangle

6. Question

Hint

Great Work!

Cosine Rule (finding a length)

Cosine Rule (finding an angle)

Remember

Labelling the triangle

7. Question

Excellent!

Remember

Labelling the triangle

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