In a triangle what is always opposite of the shortest side?
The smallest angle is always opposite the smallest side,
the largest angle is always opposite the largest side, etc
Reiny is correct
These are the answer choices, please help:
A the longest side
B the middle side
C the greatest angle
D the least angle
In a triangle, the side that is always opposite to the shortest side is the smallest angle. To understand why this is true, let's go through the steps:
Step 1: Identify the lengths of the sides of the triangle.
Step 2: Find the shortest side by comparing the lengths of all three sides.
Step 3: Identify the angles of the triangle corresponding to each side.
Each angle of a triangle corresponds to the side opposite it. So, the side that is opposite the shortest side will be opposite the smallest angle.
To find the smallest angle, we can use one of two methods:
Method 1: Use the Law of Sines
The Law of Sines states that in any triangle, the ratio of a side length to the sine of its opposite angle is constant. Using this law, you can calculate the angles of the triangle and identify the smallest angle. The side opposite to the smallest angle will be the side we are looking for.
Method 2: Use the Triangle Inequality Theorem
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this theorem, you can compare the lengths of the sides to determine the smallest side and its corresponding angle.
By using either method, you should be able to identify the smallest angle and the side opposite it, which is always the side opposite the shortest side in a triangle.