Area of Non-Right Angled Triangles 1

Question 1 of 4

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

Round your answer to the nearest

c m^{2}

$cm^2$

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

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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 = 35

$b=35$ cm

c = 22

$c=22$ cm

A = 41 °

$A=41°$

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

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $35$ $35$ $) ($ $)($ $22$ $22$ $) \sin 41 °$ $)sin\color(purple)(41°)$	Substitute the values

	$=$ $=$	$\frac{1}{2} (770) \sin 41 °$ $1/2(770)sin41°$	Simplify

	$=$ $=$	$385 \times \sin 41 °$ $385timessin41°$	Evaluate $\sin$ $sin$ $41$ $41$ on your calculator
	$=$ $=$	$252.5827$ $252.5827$
	$=$ $=$	$253 c m^{2}$ $253cm^2$	Rounded off to the nearest $c m^{2}$ $cm^2$

253 c m^{2}

$253 cm^2$

Question 2 of 4

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

Round your answer to one decimal place

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

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Area of a Non-Right Angled Triangle

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $a$ $a$ $c$ $c$

\sin

$sin$ $B$ $B$

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}

$A_triangle=1/2$ $a$ $a$ $c$ $c$

\sin

$sin$ $B$ $B$

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

a = 33

$a=33$ cm

c = 24

$c=24$ cm

B = 110 °

$B=110°$

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

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $33$ $33$ $) ($ $)($ $24$ $24$ $) \sin 110 °$ $)sin\color(purple)(110)°$	Substitute

	$=$ $=$	$\frac{1}{2} (792) \sin 110 °$ $1/2(792)sin110°$	Evaluate $\sin$ $sin$ $110$ $110$ on your calculator

	$=$ $=$	$396 \times 0.9396926$ $396times0.9396926$
	$=$ $=$	$372.118$ $372.118$
	$=$ $=$	$372.1 c m^{2}$ $372.1 cm^2$	Rounded off to one decimal place

372.1 c m^{2}

$372.1 cm^2$

Question 3 of 4

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

Round your answer to one decimal place

(120.5) $m m^{2}$ $mm^2$

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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 = 18

$b=18$ mm

c = 14

$c=14$ mm

A = 73 °

$A=73°$

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

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $18$ $18$ $) ($ $)($ $14$ $14$ $) \sin$ $)sin$ $73 °$ $73°$	Substitute the values

	$=$ $=$	$\frac{1}{2} (252) \sin 73 °$ $1/2(252)sin73°$	Evaluate $\sin$ $sin$ $73$ $73$ on your calculator

	$=$ $=$	$126 \times 0.956305$ $126times0.956305$
	$=$ $=$	$120.494$ $120.494$
	$=$ $=$	$120.5 m m^{2}$ $120.5 mm^2$	Rounded off to one decimal place

120.5 m m^{2}

$120.5 mm^2$

Question 4 of 4

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

Round your answer to

1

$1$ decimal place

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

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Area of a Non-Right Angled Triangle

A_{△} = \frac{1}{2}

$A_triangle=1/2$ $a$ $a$ $c$ $c$

\sin

$sin$ $B$ $B$

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}

$A_triangle=1/2$ $a$ $a$ $c$ $c$

\sin

$sin$ $B$ $B$

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

a = 18

$a=18$ cm

c = 27

$c=27$ cm

B = 39 °

$B=39°$

$A_{△}$ $A_triangle$	$=$ $=$	$\frac{1}{2}$ $1/2$ $a$ $a$ $c$ $c$ $\sin$ $sin$ $B$ $B$

	$=$ $=$	$\frac{1}{2} ($ $1/2($ $18$ $18$ $) ($ $)($ $27$ $27$ $) \sin$ $)sin$ $39 °$ $39°$	Substitute the values

	$=$ $=$	$\frac{1}{2} (486) \sin 39 °$ $1/2(486)sin39°$	Evaluate $\sin$ $sin$ $39$ $39$ on your calculator

	$=$ $=$	$243 \times 0.62932$ $243times0.62932$
	$=$ $=$	$152.925$ $152.925$
	$=$ $=$	$152.9 c m^{2}$ $152.9 cm^2$	Rounded off to one decimal place

152.9 c m^{2}

$152.9 cm^2$

Area of Non-Right Angled Triangles 1

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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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