Processing math: 100%

hacklink al hack forum organik hit kayseri escort sex izle meritking sekabet giriş grandpashabet grandpashabet betting utan svensk licens Queenbet giriş sekabet sekabet Holiganbet interbahis sekabet casibom casibom giriş donami bonasi voren satolir bettilt vozol türkiye casibom marsbahis onwin onwin casibom güncel giriş deneme bonusu veren siteler kumar siteleri casino metropol casinomaxi jojobet casibom kumar siteleri starzbet bahis siteleri casino siteleri betwoon starzbet dinitme binissi virin sitolar dinitme binissi virin sitolar betsat giriş Superbet bahsegel giriş deneme bonusu veren siteler bodrum travesti betcio dinamobet 1xbet jojobet sahabet jojobet güncel giriş donami bonasi voren satolit casibom casibom betturkey meritking betcio giriş makrobet ultrabet giriş pornhub now galabet zbahis betturkey perabet giriş perabet giriş matbet giriş romabet giriş vbettr

Topics

>

>

>

Law of Sines: Solving for an Angle

>

Law of Sines: Solving for an Angle

Law of Sines: Solving for an Angle

Try VividMath Premium to unlock full access

Start Free Trial

Loading...

Lets see your results!

Points

Score

Time

1
2
3
4
5

Answered
Review

Question 1 of 5

Find

$theta$

Round your answer to the nearest minute

$theta=$ (67) $°$ (32) $'$

Incorrect

Need Text

Swarmify Video Hosting

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Sine Law

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}=\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}=\frac{\color{#9a00c7}{c}}{\sin\color{#9a00c7}{C}}$

where:
$a$ is the side opposite angle $A$
$b$ is the side opposite angle $B$
$c$ is the side opposite angle $C$

When to use the Sine Law (for non-right angled triangles)

a) Given 2 sides and 1 angle to find the other angle

or

b) Given 2 angles 1 side to find the other side

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

Shift or 2nd F or INV

$=$ Inverse function

$=$

$=$ Equal function

Degree-to-Minute Conversion

$1$ degree

$=60$ minutes

Minute-to-Second Conversion

$1$ minute

$=60$ seconds

Rounding Off to the Nearest Minute

If the seconds is greater than or equal to $30”$ , round the minute up.
If the seconds is less than $30”$ , round the minute down.

First, label the triangle according to the Sine Law.

Substitute the three known values to the Sine Law to find the fourth missing value.

From labelling the triangle, we know that the known values are those with labels

$b, B, c$ and

$C$ .

$b=29 cm$

$B=theta$

$c=18 cm$

$C=35°$

$\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}$	$=$	$\frac{\color{#9a00c7}{c}}{\sin\color{#9a00c7}{C}}$

$\frac{\color{#00880A}{29}}{\sin\color{#00880A}{\theta}}$	$=$	$\frac{\color{#9a00c7}{18}}{\sin\color{#9a00c7}{35°}}$	Substitute the values

$18timessintheta$	$=$	$29timessin35°$	Cross multiply
$18timessintheta$ $divide18$	$=$	$29timessin35°$ $divide18$	Divide both sides by $18$

$sintheta$	$=$	$(29timessin35°)/18$

$sintheta$	$=$	$16.632717/18$	Use the calculator to simplify

$sintheta$	$=$	$0.9240954$
$theta$	$=$	$sin^(-1)0.9240954$	$sin$ inverse

Simplify this further by evaluating

$sin^(-1)0.9240954$ using the calculator:

$1.$ Press Shift or 2nd F (depending on your calculator)

$2.$ Press $sin$

$3.$ Press

$0.9240954$

$4.$ Press $=$

The result will be:

$67.5323°$

Round off the answer to the nearest minute.

$theta$	$=$	$67.5323°$
	$=$	$67°31’56”$	Press DMS on your calculator
	$=$	$67°32’$	Round up since the seconds is greater than $30”$

$67°32’$

Question 2 of 5

Find

$theta$

Round your answer to the nearest degree

$theta=$ (62) $°$

Incorrect

Need Text

Swarmify Video Hosting

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Sine Law

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}=\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}=\frac{\color{#9a00c7}{c}}{\sin\color{#9a00c7}{C}}$

where:
$a$ is the side opposite angle $A$
$b$ is the side opposite angle $B$
$c$ is the side opposite angle $C$

When to use the Sine Law (for non-right angled triangles)

a) Given 2 sides and 1 angle to find the other angle

or

b) Given 2 angles 1 side to find the other side

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

Shift or 2nd F or INV

$=$ Inverse function

$=$

$=$ Equal function

Degree-to-Minute Conversion

$1$ degree

$=60$ minutes

Minute-to-Second Conversion

$1$ minute

$=60$ seconds

Rounding Off to the Nearest Minute

If the seconds is greater than or equal to $30”$ , round the minute up.
If the seconds is less than $30”$ , round the minute down.

First, label the triangle according to the Sine Law.

Substitute the three known values to the Sine Law to find the fourth missing value.

From labelling the triangle, we know that the known values are those with labels

$p, P, r$ and

$R$ .

$p=92 m$

$P=24°$

$r=200 m$

$R=theta$

$\frac{\color{#007DDC}{p}}{\sin\color{#007DDC}{P}}$	$=$	$\frac{\color{#9a00c7}{r}}{\sin\color{#9a00c7}{R}}$

$\frac{\color{#007DDC}{92}}{\sin\color{#007DDC}{24°}}$	$=$	$\frac{\color{#9a00c7}{200}}{\sin\color{#9a00c7}{\theta}}$	Substitute the values

$92timessintheta$	$=$	$200timessin24°$	Cross multiply
$92timessintheta$ $divide92$	$=$	$200timessin24°$ $divide92$	Divide both sides by $92$

$sintheta$	$=$	$(200timessin24°)/92$

$sintheta$	$=$	$81.34733/92$	Use the calculator to simplify

$sintheta$	$=$	$0.88421$
$theta$	$=$	$sin^(-1)0.88421$	$sin$ inverse

Simplify this further by evaluating

$sin^(-1)0.88421$ using the calculator:

$1.$ Press Shift or 2nd F (depending on your calculator)

$2.$ Press $sin$

$3.$ Press

$0.88421$

$4.$ Press $=$

The result will be:

$62.15447°$

Round off the answer to the nearest degree.

$theta$	$=$	$62.15447°$
	$=$	$62°9’16”$	Press DMS on your calculator
	$=$	$62°$	Round down since the minutes is less than $30’$

$62°$

Question 3 of 5

Find

$theta$

Round your answer to the nearest degree

$theta=$ (74) $°$

Incorrect

Need Text

Swarmify Video Hosting

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Sine Law

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}=\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}=\frac{\color{#9a00c7}{c}}{\sin\color{#9a00c7}{C}}$

where:
$a$ is the side opposite angle $A$
$b$ is the side opposite angle $B$
$c$ is the side opposite angle $C$

When to use the Sine Law (for non-right angled triangles)

a) Given 2 sides and 1 angle to find the other angle

or

b) Given 2 angles 1 side to find the other side

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

Shift or 2nd F or INV

$=$ Inverse function

$=$

$=$ Equal function

Degree-to-Minute Conversion

$1$ degree

$=60$ minutes

Minute-to-Second Conversion

$1$ minute

$=60$ seconds

Rounding Off to the Nearest Minute

If the seconds is greater than or equal to $30”$ , round the minute up.
If the seconds is less than $30”$ , round the minute down.

Since the values given are opposite each other, we can directly substitute them to the Sine Law.

$a=51.4 m$

$A=theta$

$b=52.9 m$

$B=82°$

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}$	$=$	$\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}$

$\frac{\color{#007DDC}{51.4}}{\sin\color{#007DDC}{\theta}}$	$=$	$\frac{\color{#00880A}{52.9}}{\sin\color{#00880A}{82°}}$	Substitute the values

$52.9timessintheta$	$=$	$51.4timessin82°$	Cross multiply
$52.9timessintheta$ $divide52.9$	$=$	$51.4timessin82°$ $divide52.9$	Divide both sides by $52.9$

$sintheta$	$=$	$(51.4timessin82°)/52.9$

$sintheta$	$=$	$(51.4times0.990268)/52.9$	Use the calculator to simplify

$sintheta$	$=$	$50.8997787/52.9$

$sintheta$	$=$	$0.9621886$
$theta$	$=$	$sin^(-1)0.9621886$	$sin$ inverse

Simplify this further by evaluating

$sin^(-1)0.9621886$ using the calculator:

$1.$ Press Shift or 2nd F (depending on your calculator)

$2.$ Press $sin$

$3.$ Press

$0.9621886$

$4.$ Press $=$

The result will be:

$74.1938°$

Round off the answer to the nearest degree.

$theta$	$=$	$74.1938°$
	$=$	$74°11’$	Press DMS on your calculator
	$=$	$74°$	Round down since the minutes is less than $30’$

$74°$

Question 4 of 5

Find the obtuse angle

$alpha$

Round your answer to the nearest degree

$alpha=$ (131) $°$

Incorrect

Need Text

Swarmify Video Hosting

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Sine Law

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}=\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}=\frac{\color{#9a00c7}{c}}{\sin\color{#9a00c7}{C}}$

where:
$a$ is the side opposite angle $A$
$b$ is the side opposite angle $B$
$c$ is the side opposite angle $C$

When to use the Sine Law (for non-right angled triangles)

a) Given 2 sides and 1 angle to find the other angle

or

b) Given 2 angles 1 side to find the other side

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

Shift or 2nd F or INV

$=$ Inverse function

$=$

$=$ Equal function

Degree-to-Minute Conversion

$1$ degree

$=60$ minutes

Minute-to-Second Conversion

$1$ minute

$=60$ seconds

Rounding Off to the Nearest Minute

If the seconds is greater than or equal to $30”$ , round the minute up.
If the seconds is less than $30”$ , round the minute down.

Substitute the three known values to the Sine Law to find the fourth missing value.

$a=37$ m

$A=alpha$

$b=16$ m

$B=19°$

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}$	$=$	$\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}$

$\frac{\color{#007DDC}{37}}{\sin\color{#007DDC}{\alpha}}$	$=$	$\frac{\color{#00880A}{16}}{\sin\color{#00880A}{19}}$	Substitute the values

$16timessinalpha$	$=$	$37timessin19°$	Cross multiply
$16timessinalpha$ $divide16$	$=$	$37timessin19°$ $divide16$	Divide both sides by $16$

$sinalpha$	$=$	$(37timessin19°)/16$

$sinalpha$	$=$	$12.0460217/16$	Use the calculator to simplify

$sinalpha$	$=$	$0.75287636$
$alpha$	$=$	$sin^(-1)0.75287636$	$sin$ inverse

Simplify this further by evaluating

$sin^(-1)0.75287636$ using the calculator:

$1.$ Press Shift or 2nd F (depending on your calculator)

$2.$ Press $sin$

$3.$ Press

$0.75287636$

$4.$ Press $=$

The result will be:

$48.8401549°$

Round off the answer to the nearest degree.

$alpha$	$=$	$48.8401549°$
	$=$	$48°50’$	Press DMS on your calculator
	$=$	$49°$	Round up since the minutes is greater than $30’$

Notice that the result is an acute angle even though the actual angle is supposedly obtuse. This is because we used the Sine Law.

To get the obtuse angle, simply subtract the angle from

$180°$ .

$alpha$	$=$	$180-49$
$alpha$	$=$	$131°$

$131°$

Question 5 of 5

Find the obtuse angle

$alpha$

Round your answer to the nearest degree

$alpha=$ (150) $°$

Incorrect

Need Text

Swarmify Video Hosting

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Sine Law

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}=\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}=\frac{\color{#9a00c7}{c}}{\sin\color{#9a00c7}{C}}$

where:
$a$ is the side opposite angle $A$
$b$ is the side opposite angle $B$
$c$ is the side opposite angle $C$

When to use the Sine Law (for non-right angled triangles)

a) Given 2 sides and 1 angle to find the other angle

or

b) Given 2 angles 1 side to find the other side

Calculator Buttons to Use

$sin$

$=$ Sine function

$cos$

$=$ Cosine function

$tan$

$=$ Tangent function

DMS or $° ‘ ‘ ‘$

$=$ Degree/Minute/Second

Shift or 2nd F or INV

$=$ Inverse function

$=$

$=$ Equal function

Degree-to-Minute Conversion

$1$ degree

$=60$ minutes

Minute-to-Second Conversion

$1$ minute

$=60$ seconds

Rounding Off to the Nearest Minute

If the seconds is greater than or equal to $30”$ , round the minute up.
If the seconds is less than $30”$ , round the minute down.

Substitute the three known values to the Sine Law to find the fourth missing value.

$a=128$ m

$A=alpha$

$b=99$ m

$B=23°$

$\frac{\color{#007DDC}{a}}{\sin\color{#007DDC}{A}}$	$=$	$\frac{\color{#00880A}{b}}{\sin\color{#00880A}{B}}$

$\frac{\color{#007DDC}{128}}{\sin\color{#007DDC}{\alpha}}$	$=$	$\frac{\color{#00880A}{99}}{\sin\color{#00880A}{23}}$	Substitute the values

$99timessinalpha$	$=$	$128timessin23°$	Cross multiply
$99timessinalpha$ $divide99$	$=$	$128timessin23°$ $divide99$	Divide both sides by $99$

$sinalpha$	$=$	$(128timessin23°)/99$

$sinalpha$	$=$	$50.013584/99$	Use the calculator to simplify

$sinalpha$	$=$	$0.5051877$
$alpha$	$=$	$sin^(-1)0.5051877$	$sin$ inverse

Simplify this further by evaluating

$sin^(-1)0.5051877$ using the calculator:

$1.$ Press Shift or 2nd F (depending on your calculator)

$2.$ Press $sin$

$3.$ Press

$0.5051877$

$4.$ Press $=$

The result will be:

$30.343815°$

Round off the answer to the nearest degree.

$alpha$	$=$	$30.343815°$
	$=$	$30°20’$	Press DMS on your calculator
	$=$	$30°$	Round down since the minutes is less than $30’$

Notice that the result is an acute angle even though the actual angle is supposedly obtuse. This is because we used the Sine Law.

To get the obtuse angle, simply subtract the angle from

$180°$ .

$alpha$	$=$	$180-30$
$alpha$	$=$	$150°$

$150°$