If sides A and B of a triangle have lengths of 5 and 9 respectively, and the angle between them is $\frac{π}{4}$ $(pi)/4$ , then what is the area of the triangle?

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If sides A and B of a triangle have lengths of 5 and 9 respectively, and the angle between them is $\frac{π}{4}$ $(pi)/4$ , then what is the area of the triangle?

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Answer 1 · 2016-03-19T10:58:39

$\frac{45 \sqrt{2}}{4} \approx 15.91 square units$ $( 45sqrt2)/4 ≈ 15.91" square units "$

Explanation:

Given a triangle , where 2 sides and the angle between them are known, then the area of the triangle can be calculated using

Area = $\frac{1}{2} A B sin θ$ $1/2 ABsintheta$

where A and B are the 2 sides and $θ$ $theta$ , the angle between them

here A = 5 , B = 8 and $θ = \frac{π}{4}$ $theta = pi/4$

hence area $= \frac{1}{2} \times 5 \times 9 \times sin (\frac{π}{4}) = \frac{45}{2 \sqrt{2}}$ $= 1/2xx5xx9xxsin(pi/4) = 45/(2sqrt2)$

where the exact value of $sin (\frac{π}{4}) = \frac{1}{\sqrt{2}}$ $sin(pi/4) = 1/sqrt2$

Rationalising the denominator of the fraction, to obtain

area $= \frac{45}{2 \sqrt{2}} = \frac{45 \sqrt{2}}{4} \approx 15.91 square units$ $= 45/(2sqrt2) = (45sqrt2)/4 ≈ 15.91" square units "$

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If sides A and B of a triangle have lengths of 5 and 9 respectively, and the angle between them is $\frac{π}{4}$ $(pi)/4$ , 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 5 and 9 respectively, and the angle between them is (pi)/4π4(pi)/4, then what is the area of the triangle?

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If sides A and B of a triangle have lengths of 5 and 9 respectively, and the angle between them is $\frac{π}{4}$ $(pi)/4$ , then what is the area of the triangle?