Try to draw a triangle with side lengths of 3 Cm and 6 cm and an included angle of 120 degrees. Do given segments and angles produce a unique triangle, more than one triangle,or no triangle.
What is the answer, I don't get it
i still don’t get it :p
To determine if a triangle can be formed with the given side lengths and included angle, we can use the Law of Cosines. The Law of Cosines states that, in a triangle with sides a, b, and c, and angle C opposite side c:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's substitute the given values into the equation to check if a triangle can be formed:
c^2 = 3^2 + 6^2 - 2 * 3 * 6 * cos(120°)
Simplifying,
c^2 = 9 + 36 - 36 * cos(120°)
cos(120°) = -1/2, so
c^2 = 9 + 36 - 36 * (-1/2)
c^2 = 9 + 36 + 18
c^2 = 63
Taking the square root of both sides,
c = √63
So, c ≈ 7.937 cm
Now, to determine if a triangle can be formed, we compare the sum of the two shorter side lengths with the length of the longest side:
Sum of shorter sides = 3 + 6 = 9 cm
Since the sum of the shorter sides (9 cm) is greater than the length of the longest side (7.937 cm), a triangle can be formed.
Therefore, the given segments and angle produce a unique triangle.
I did it!
What did you do?