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Mathematics
Mensuration
Area of a Triangular Region - Given Two Sides and Included Angle
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Multiple Choice
Which formula is used to find the area of a triangle when two sides and the included angle are given?
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$\text{Area} = \frac{1}{2} \times a \times c \times \sin B$
$\text{Area} = \frac{1}{2} \times a \times b \times \sin C$
$\text{Area} = a \times b \times \cos C$
$\text{Area} = \frac{1}{2} \times c \times b \times \sin A$
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When given sides $b$ and $c$ and included angle $A$, what is the formula for the area of the triangle?
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$\frac{1}{2} \times b \times c \times \sin A$
$\frac{1}{2} \times b \times a \times \sin C$
$b \times c \times \cos A$
$\frac{1}{2} \times a \times b \times \cos C$
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What is the correct formula for the area of a triangle when two sides $a$ and $c$, and their included angle $B$ are known?
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$\frac{1}{2} \times c \times a \times \sin B$
$a \times c \times \sin B$
$\frac{1}{2} \times a \times c \times \cos B$
$\frac{1}{2} \times b \times c \times \sin A$
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For a triangle with sides $a = 5$, $b = 7$, and included angle $C = 45^\circ$, which formula calculates its area?
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$\frac{1}{2} \times 5 \times 7 \times \sin 45^\circ$
$5 \times 7 \times \cos 45^\circ$
$\frac{1}{2} \times 5 \times 7 \times \cos 45^\circ$
$\frac{1}{2} \times 7 \times 5 \times \sin 45^\circ$
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If $BC = 8$, $CA = 10$, and $\angle C = 30^\circ$, what is the area of the triangle?
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20 units
40 units
20 square units
40 square units
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