Question

A 30°–60°–90° triangle has a shorter leg with a length of 3 units.

What is the length of the hypotenuse of the triangle?

Answer 1

so its \[\sqrt{3}\]

Answer 2

No. The figure above shows the ratios of the lengths of the sides.
Look at the figure. When the short leg is 1, the long leg is \(\sqrt{3} \), and the hypotenuse is 2.

Since in your case the short leg is 3, and that is 3 times larger than the short leg of the figure, then the long leg and the hypotenuse are also 3 times longer. Also, notice you are asked for the length of the hypotenuse, not the long leg.

Answer 3

i dont get it

Answer 4

Ok.
I'll explain better.

Answer 5

In a 30-60-90 degree triangle, you have a right angle (the 90-degree angle).
That makes the triangle a right triangle.
The longest side is the side opposite the right angle. It is called the hypotenuse.

Ok so far?

Answer 6

The two sides that form the right angle are called the legs.
The two legs are shorter than the hypotenuse.
The shorter leg is opposite the 30-degree angle.
The longer leg is opposite the 60-degree angle.

Answer 7

In a 30-60-90 triangle, the ratio of the lengths of the sides is:

short leg : long leg : hypotenuse

\(1 : \sqrt{3} : 2\)

That means if the short leg measures 1, the longer leg measures \(\sqrt{3} \), and the hypotenuse measures 2, or twice the length of the short leg.

Answer 8

In your case, the short leg measures 3.
The hypotenuse is twice the short leg.
What is 2 * 3?