MHB Area of Triangle ABC: Find the Solution

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To find the area of triangle ABC with sides AC = 4 cm, AB = 3 cm, and angle A = 60 degrees, the formula A = 1/2 * a * b * sin(θ) is applicable. Substituting the values, the area can be calculated as A = 1/2 * 4 * 3 * sin(60°). The sine of 60 degrees is √3/2, leading to an area of 6√3/4 cm², which simplifies to approximately 2.598 cm². The height from point C can also be derived using the area formula, confirming the calculations.
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ABC is a triangle. AC=4cm; AB=3cm; A=60 degrees.
I need help finding the area of triangle ABC.
 
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Can you calculate the height from point C ?
 
If you know the lengths of two sides of a triangle (we'll call them \(a\) and \(b\)), and the angle \(\theta\) subtended by the two sides, then the area \(A\) of the triangle is given by:

$$A=\frac{1}{2}ab\sin(\theta)$$

Can you proceed?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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