A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ . If side C has a length of $15$ $15$ 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 $\frac{π}{4}$ $pi/4$ . If side C has a length of $15$ $15$ 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 · 2016-04-13T10:58:50

The length of side A is $5.49$ $5.49$ units

Explanation:

The opposite angle of the side C is $∠ C = \frac{π}{4} = \frac{180}{4} = 45^{0}$ $/_C=pi/4=180/4=45^0$
The opposite angle of the side A is $∠ A = \frac{π}{12} = \frac{180}{4} = 15^{0}$ $/_A=pi/12=180/4=15^0$
Using sine law we get $\frac{A}{sin A} = \frac{C}{sin C} or A = C \cdot (\frac{sin A}{sin C}) or A = 15 \cdot (\frac{sin 15}{sin 45}) = 5.49$ $A/sinA=C/sinC or A= C*(sinA/sinC) or A=15*(sin15/sin45)=5.49$ units [Ans]

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ . If side C has a length of $15$ $15$ 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 π4pi/4. If side C has a length of 1515 and the angle between sides B and C is π12pi/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 $\frac{π}{4}$ $pi/4$ . If side C has a length of $15$ $15$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?