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 55, 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 55, what is the area of the triangle?

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Answer 1 · 2016-03-01T21:22:25

≈ 405.268 square units

Explanation:

Since the angle between A and B is $\frac{π}{2} this is a right triangle with C ,the hypotenuse$ $pi/2" this is a right triangle with C ,the hypotenuse "$
area of triangle = $\frac{1}{2} A B$ $1/2AB$
Require to find A. This can be done using basic tangent ratio.

$tan (\frac{π}{12}) = \frac{A}{B} \Rightarrow A = B tan (\frac{π}{12}) = 55 tan (\frac{π}{12}) \approx 14.737$ $tan(pi/12) = A/B rArr A = Btan(pi/12) = 55tan(pi/12) ≈ 14.737$

$\Rightarrow area = \frac{1}{2} \times 55 \times 14.737 \approx 405.268 square units$ $rArr " area " = 1/2xx55xx14.737 ≈ 405.268" square units "$

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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 55, 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 55, what is the area of the triangle?