If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is $\frac{5 π}{8}$ $(5pi)/8$ , then what is the area of the triangle?

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If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is $\frac{5 π}{8}$ $(5pi)/8$ , then what is the area of the triangle?

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Answer 1 · 2016-10-02T13:47:23

$11.09$ $11.09$

Explanation:

$Let's consider the diagram$ $"Let's consider the diagram"$

enter image source here

$I have mentioned$ $"I have mentioned"$ $\frac{5 π}{8}$ $(5pi)/8$ $as$ $"as"$ ${112.5}^{\circ}$ $112.5^circ$

$We can find the area of a triangle given the length of two sides$ $"We can find the area of a triangle given the length of two sides"$
$and the angle between them using this formula$ $"and the angle between them using this formula"$

$color(blue)($ $Area$ $color(blue)("Area"$ $= \frac{1}{2} \cdot$ $color(blue)(=1/2*"$ $A$ $color(blue)("A"$ $\cdot$ $color(blue)(*$ $B$ $color(blue)("B"$ $\cdot sin (c)$ $"color(blue)(*sin(c)$

$\to \frac{1}{2} \cdot 8 \cdot 3 \cdot sin (112.5)$ $rarr1/2*8*3*sin(112.5)$

$rarr1/cancel2^1*cancel24^12*sin(112.5)$

$rarr12*sin(112.5)$

$rarr12*0.92$

$color(green)(rArr11.09$

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If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is $\frac{5 π}{8}$ $(5pi)/8$ , then what is the area of the triangle?

1 Answer

Explanation:

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If sides A and B of a triangle have lengths of 8 and 3 respectively, and the angle between them is $\frac{5 π}{8}$ $(5pi)/8$ , then what is the area of the triangle?