# If sides A and B of a triangle have lengths of 3 and 5 respectively, and the angle between them is #(pi)/3#, then what is the area of the triangle?

The area of the triangle is

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Using the formula for the area of a triangle, which is ( \frac{1}{2} \times \text{base} \times \text{height} ), and knowing that the height of the triangle is given by ( A \times \sin(\theta) ), where ( A ) is the length of side ( A ) and ( \theta ) is the angle between sides ( A ) and ( B ), we can calculate the area of the triangle. Therefore, the area of the triangle is ( \frac{1}{2} \times 5 \times 3 \times \sin\left(\frac{\pi}{3}\right) ). Evaluating this expression yields an area of ( \frac{15\sqrt{3}}{4} ) square units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has sides A, B, and C. Sides A and B are of lengths #5# and #2#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?
- A triangle has sides A, B, and C. The angle between sides A and B is #(2pi)/3#. If side C has a length of #2 # and the angle between sides B and C is #pi/12#, what is the length of side A?
- If #A = <1 ,6 ,-8 >#, #B = <-9 ,4 ,1 ># and #C=A-B#, what is the angle between A and C?
- How do you determine whether #triangle ABC# has no, one, or two solutions given #A=44^circ, a=14, b=19#?
- If sides A and B of a triangle have lengths of 5 and 6 respectively, and the angle between them is #(pi)/2#, then what is the area of the triangle?

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