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

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

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Answer 1 · 2016-02-22T21:47:00

≈ 1.34 units

Explanation:

This is a right triangle.

since $\frac{5 π}{12} + \frac{π}{12} = \frac{6 π}{12} = \frac{π}{2}$ $(5pi)/12 + pi/12 = (6pi)/12 = pi/2$

hence the angle between A and C $= π - \frac{π}{2} = \frac{π}{2}$ $= pi - pi/2 = pi/2$

To find A then , use $tangent trig ratio$ $color(blue)" tangent trig ratio "$

$\Rightarrow tan (\frac{π}{12}) = \frac{A}{C} \Rightarrow A = C tan (\frac{π}{12}) = 5 tan (\frac{π}{12}) \approx 1.34$ $rArr tan(pi/12) = A/C rArr A = Ctan(pi/12) = 5tan(pi/12) ≈ 1.34$

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

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