A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, 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 $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, what is the area of the triangle?

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Answer 1 · 2015-12-30T23:32:29

$A r e a = S = 19.292$ $Area = S = 19.292$

Explanation:

If the angle between A and B is $\frac{π}{2}$ $pi/2$ then the triangle is a right one and its area is:
$S = \frac{A \cdot B}{2}$ $S = (A*B)/2$

Since the angle between B and C is known and the length of B also is known, we can find A in this way:
$tan (\frac{π}{12}) = \frac{opposed cathetus}{adjacent cathetus}$ $tan (pi/12) = ("opposed cathetus")/("adjacent cathetus")$
So $tan (\frac{π}{12}) = \frac{A}{B}$ $tan (pi/12) = A/B$ => $A = B \cdot tan (\frac{π}{12})$ $A = B*tan(pi/12)$

Finally,
$S = \frac{B^{2} \cdot tan (\frac{π}{12})}{2}$ $S = (B^2*tan(pi/12))/2$
$S = \frac{12^{2} \cdot 0.267949}{2} = 19.292$ $S = (12^2*0.267949)/2 = 19.292$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, 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 π2(pi)/2 and the angle between sides B and C is π12pi/12. If side B has a length of 12, 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 $\frac{π}{2}$ $(pi)/2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 12, what is the area of the triangle?