MHB Area of Triangle ABC: Find the Solution

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SUMMARY

The area of triangle ABC can be calculated using the formula \(A=\frac{1}{2}ab\sin(\theta)\), where \(a\) and \(b\) are the lengths of two sides, and \(\theta\) is the angle between them. For triangle ABC, with sides AC=4cm, AB=3cm, and angle A=60 degrees, the area is determined by substituting these values into the formula. The height from point C can also be derived using the area once calculated.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine.
  • Familiarity with the formula for the area of a triangle.
  • Basic knowledge of triangle properties and geometry.
  • Ability to perform calculations involving angles and side lengths.
NEXT STEPS
  • Learn how to derive the height of a triangle using area calculations.
  • Study the Law of Sines for solving triangles with known angles and sides.
  • Explore the properties of triangles, including the relationship between angles and side lengths.
  • Investigate different methods for calculating the area of triangles, such as Heron's formula.
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in solving problems related to triangle properties and area calculations.

STS
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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?
 

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