A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 48, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 48, what is the area of the triangle?

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Answer 1 · 2016-01-28T07:38:41

4299.322531

Explanation:

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lets draw a perpendicular line on B .
suppose, the length of the perpendicular is D
now, the problem says, the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$
now,
in, $△ A B D$ $triangleABD$ ,
$\frac{D}{B} = tan (\frac{5 π}{12})$ $D/B=tan((5pi)/12)$
$or, D = B tan (\frac{5 π}{12})$ $or,D=Btan((5pi)/12)$
now, by putting the values, B=48 and tan $\frac{5 π}{12}$ $(5pi)/12$ ,
$D = 48 \cdot 3.732050808$ $D=48*3.732050808$
$or, D = 179.1384388$ $or, D=179.1384388$
so,
The area of $△ A B C = \frac{1}{2} \cdot B \cdot D$ $triangleABC=1/2*B*D$
now, by putting the value of B and D in the above equation, we get,
$△ A B C = \frac{1}{2} \cdot 48 \cdot 179.1384388 = 4299.322531$ $triangleABC=1/2*48*179.1384388=4299.322531$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 48, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{12}$ $(5pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 48, what is the area of the triangle?