MHB Area of Triangle ABC: Find the Solution

  • Thread starter Thread starter STS
  • Start date Start date
  • Tags Tags
    Area Triangle
AI Thread Summary
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.
STS
Messages
5
Reaction score
0
ABC is a triangle. AC=4cm; AB=3cm; A=60 degrees.
I need help finding the area of triangle ABC.
 
Mathematics news on Phys.org
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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...

Similar threads

Replies
17
Views
2K
Replies
5
Views
2K
Replies
3
Views
2K
Replies
4
Views
2K
Replies
4
Views
1K
Replies
1
Views
1K
Back
Top