Question

The hypotenuse of a 30o-60o-90o triangle measures 4 square 3 inches. What is the length of the shorter leg?

Answer 1

The shorter leg is
`2√(3)` inches

Step-by-step explanation:

The 30°-60°-90° is a special type of right-angled triangles

It has the following special side length:

The length of the side opposite to the 30° is
`(1)/(2)` the length of the hypotenuse

The length of the side opposite to the 60° is
`(√(3) )/(2)` of the hypotenuse

Now, we know that the lengths of the sides in a triangle are proportional to the angles

This means that the shortest side will be the one opposite to the smallest angles

In our case, the shortest side will be the one opposite to the 30° angle

We are given that the hypotenuse of the triangle is
`4√(3)` in

From the above:

Shorter leg = leg opposite to 30° =
`(1)/(2) * hypotenuse = (1)/(2) * 4√(3) = 2√(2)` inches

Hope this helps :)