Constructing Given 3 Sides and 2 Included Angles A triangle is a polygon with three sides and three angles. We can construct a triangle if we have the me...
A triangle is a polygon with three sides and three angles. We can construct a triangle if we have the measurements of its three sides. However, in most cases, we are given the lengths of two sides and one angle. In this case, we need to find the third side length and the other angles.
There are two main methods for constructing a triangle given the lengths of two sides and one angle:
Method 1: Using the Heron's Formula
The Heron's Formula allows us to calculate the length of the third side of a triangle given the lengths of its two sides.
H = (s - a)(s - b)(s - c) / 4
where:
H is the length of the third side
a and b are the lengths of the two given sides
c is the length of the unknown side
Method 2: Using the Pythagorean theorem
The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
a² + b² = c²
Constructing a Triangle
Once we have the lengths of the two sides and one angle, we can use one of the methods above to calculate the third side length. Then, we can use the Pythagorean theorem to find the other angles.
Examples
H = (5 - 5)(5 - 12)(5 - 12) / 4 = 6 cm
c² = a² + b² = 8² + 15² = 64 cm²
Therefore, c = 8 cm
Conclusion
By following either of these methods, we can construct a triangle given the lengths of its three sides and one angle