Area of Non-Right Angled Triangles 2

Question 1 of 4

Find the area of the non-right angled triangle below.

Round your answer to one decimal place

(11.25) $m^{2}$ $m^2$

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Area of a Non-Right Angled Triangle

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $b$ $b$ $c$ $c$

\sin

$sin$ $A$ $A$

where:

a

$a$ is the side opposite angle $A$ $A$

$b$ $b$ is the side opposite angle $B$ $B$
$c$ $c$ is the side opposite angle $C$ $C$

First, label the triangle.

Next, rewrite the Area formula based on the given values of the triangle.

The formula needs two sides and one angle in between them (included angle).

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $b$ $b$ $c$ $c$

\sin

$sin$ $A$ $A$

Finally, substitute the values to the revised formula and solve for the area.

b = 4.2

$b=4.2$ m

c = 7.1

$c=7.1$ m

A = 131 °

$A=131°$

$A$ $A$	$=$ $=$	$\frac{1}{2}$ $1/2$ $b$ $b$ $c$ $c$ $\sin$ $sin$ $A$ $A$

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $4.2$ $4.2$ $) ($ $)($ $7.1$ $7.1$ $) \sin$ $)sin$ $131 °$ $131°$	Substitute the values

	$=$ $=$	$\frac{1}{2} (29.82) \sin 131 °$ $1/2(29.82)sin131°$	Evaluate $\sin$ $sin$ $131$ $131$ on your calculator

	$=$ $=$	$14.91 \times 0.7547096$ $14.91times0.7547096$
	$=$ $=$	$11.2527$ $11.2527$
	$=$ $=$	$11.25 m^{2}$ $11.25 m^2$	Rounded off to two decimal places

11.25 m^{2}

$11.25 m^2$

Question 2 of 4

Find the area of the non-right angled triangle below.

Round your answer to two decimal places

(472.61) $c m^{2}$ $cm^2$

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Area of a Non-Right Angled Triangle

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $b$ $b$ $c$ $c$

\sin

$sin$ $A$ $A$

where:

a

$a$ is the side opposite angle $A$ $A$

$b$ $b$ is the side opposite angle $B$ $B$
$c$ $c$ is the side opposite angle $C$ $C$

First, label the triangle.

Next, rewrite the Area formula based on the given values of the triangle.

The formula needs two sides and one angle in between them (included angle).

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $b$ $b$ $c$ $c$

\sin

$sin$ $A$ $A$

Finally, substitute the values to the revised formula and solve for the area.

b = 33

$b=33$ cm

c = 29

$c=29$ cm

A = 99 °

$A=99°$

$A_{△}$ $A_triangle$	$=$ $=$	$\frac{1}{2}$ $1/2$ $b$ $b$ $c$ $c$ $\sin$ $sin$ $A$ $A$

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $33$ $33$ $) ($ $)($ $29$ $29$ $) \sin$ $)sin$ $99 °$ $99°$	Substitute the values

	$=$ $=$	$\frac{1}{2} (957) \sin 99 °$ $1/2(957)sin99°$	Evaluate $\sin$ $sin$ $99$ $99$ on your calculator

	$=$ $=$	$478.5 \times 0.98769$ $478.5times0.98769$
	$=$ $=$	$472.6088$ $472.6088$
	$=$ $=$	$472.61 c m^{2}$ $472.61 cm^2$	Rounded off to two decimal places

472.61 c m^{2}

$472.61 cm^2$

Question 3 of 4

Find the area of the non-right angled triangle below.

Round your answer to

2

$2$ decimal places

(305.06) $c m^{2}$ $cm^2$

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Area of a Non-Right Angled Triangle

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $r$ $r$ $q$ $q$

\sin

$sin$ $P$ $P$

where:
$r$ $r$ is the side opposite angle

R

$R$
$q$ $q$ is the side opposite angle

Q

$Q$

p

$p$ is the side opposite angle $P$ $P$

First, label the triangle.

Next, rewrite the Area formula based on the given values of the triangle.

The formula needs two sides and one angle in between them (included angle).

The included angle, $P$ $P$ , is missing, but we can find it knowing that the sum of all interior angles in a triangle is

180 °

$180°$ . Subtract the other

2

$2$ known angles from

180 °

$180°$ .

180 - (65 + 42) = 180 - 107 =

$180-(65+42)=180-107=$ $73 °$ $73°$

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $r$ $r$ $q$ $q$

\sin

$sin$ $P$ $P$

Finally, substitute the values to the revised formula and solve for the area.

r = 22

$r=22$ cm

q = 29

$q=29$ cm

P = 73 °

$P=73°$

$A_{△}$ $A_triangle$	$=$ $=$	$\frac{1}{2}$ $1/2$ $r$ $r$ $q$ $q$ $\sin$ $sin$ $P$ $P$

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $22$ $22$ $) ($ $)($ $29$ $29$ $) \sin$ $)sin$ $73 °$ $73°$	Substitute the values

	$=$ $=$	$\frac{1}{2} (638) \sin 73 °$ $1/2(638)sin73°$	Evaluate $\sin$ $sin$ $73$ $73$ on your calculator
	$=$ $=$	$319 \times 0.9563$ $319times0.9563$
	$=$ $=$	$305.06 c m^{2}$ $305.06 cm^2$	Rounded off to $2$ $2$ decimal places

305.06 c m^{2}

$305.06 cm^2$

Question 4 of 4

Find the area of the non-right angled triangle below.

Round your answer to

2

$2$ decimal places

(92.66) $c m^{2}$ $cm^2$

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Area of a Non-Right Angled Triangle

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $k$ $k$ $l$ $l$

\sin

$sin$ $J$ $J$

where:

j

$j$ is the side opposite angle $J$ $J$

$k$ $k$ is the side opposite angle $K$ $K$
$l$ $l$ is the side opposite angle $L$ $L$

First, label the triangle.

Next, rewrite the Area formula based on the given values of the triangle.

The formula needs two sides and one angle in between them (included angle).

The included angle, $J$ $J$ , is missing, but we can find it knowing that the sum of all interior angles in a triangle is

180 °

$180°$ . Subtract the other

2

$2$ known angles from

180 °

$180°$ .

180 - (38 + 79) = 180 - 117 =

$180-(38+79)=180-117=$ $63 °$ $63°$

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $k$ $k$ $l$ $l$

\sin

$sin$ $J$ $J$

Finally, substitute the values to the revised formula and solve for the area.

k = 16

$k=16$ cm

l = 13

$l=13$ cm

J = 63 °

$J=63°$

$A_{△}$ $A_triangle$	$=$ $=$	$\frac{1}{2}$ $1/2$ $k$ $k$ $l$ $l$ $\sin$ $sin$ $J$ $J$

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $16$ $16$ $) ($ $)($ $13$ $13$ $) \sin$ $)sin$ $63 °$ $63°$	Substitute the values

	$=$ $=$	$\frac{1}{2} (208) \sin 63 °$ $1/2(208)sin63°$	Evaluate $\sin$ $sin$ $63$ $63$ on your calculator
	$=$ $=$	$104 \times 0.891007$ $104times0.891007$
	$=$ $=$	$92.66 c m^{2}$ $92.66 cm^2$	Rounded off to $2$ $2$ decimal places

92.66 c m^{2}

$92.66 cm^2$

Area of Non-Right Angled Triangles 2

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1. Question

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Area of a Non-Right Angled Triangle

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Area of a Non-Right Angled Triangle

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Area of a Non-Right Angled Triangle

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Area of a Non-Right Angled Triangle

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