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 25, 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 25, what is the area of the triangle?

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Answer 1 · 2018-03-16T03:56:55

Area of the triangle $\approx 83.73$ $~~ 83.73$ sq units

Explanation:

$ˆ C = \frac{π}{2}, ˆ A = \frac{π}{12}, ˆ B = π - \frac{π}{12} - \frac{π}{2} = \frac{5 π}{12}, b = 25$ $hatC = pi / 2, hat A = pi / 12, hat B = pi - pi / 12 - pi / 2 = (5pi) / 12, b = 25$

It's a right triangle.

enter image source here

$\frac{a}{sin (\frac{π}{12})} = \frac{c}{sin (\frac{π}{2})} = \frac{25}{sin (\frac{5 π}{12})}$ $a / sin (pi/12) = c / sin (pi/2) = 25 / sin ((5pi)/12)$

$a = \frac{25 \cdot sin (\frac{π}{12})}{sin (\frac{5 π}{12})} \approx 6.7$ $a = (25 * Sin (pi/12) ) / sin((5pi)/12) ~~ 6.7$

$A r e a = (\frac{1}{2}) a \cdot b = \frac{25 \cdot 6.7}{2} \approx 83.73$ $Area = (1/2) a * b = (25 * 6.7) / 2 ~~ 83.73$

since it's a right triangle with $ˆ C = \frac{π}{2}$ $hatC = pi/2$

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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 25, what is the area of the triangle?

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Explanation:

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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 25, what is the area of the triangle?