Question

In 30,60,90 degree triangle hypotenuse is 14cm. Find length of sides opposite to angle 60​

Answer 1

Step-by-step explanation:

The sides are all of the same length - let's say a. The angles are all the same too, and since the angles must add up to 180∘, we conclude that the three angles in the equilateral triangle are equal to 180∘/3=60∘.

Now we do something sneaky. We draw a line all the way down from the top vertex of the triangle to the midpoint of the bottom line.

This new line cuts our equilateral triangle in half. What are the angles in one half?

The angle at the bottom is 90∘.

One of the angles is the same as one of the angles in the original equilateral triangle, so it is 60∘.

So the third angle must be 180∘−90∘−60∘=30∘.

Now the hypotenuse of this new triangle is a, the side length of the equilateral triangle. And the length of the shortest side is a/2, since the line we drew cut the bottom line in half.